若logx^2 y+logy^2 x=1 则y可用x表示为什么?_百度作业帮
若logx^2 y+logy^2 x=1 则y可用x表示为什么?
若logx^2 y+logy^2 x=1 则y可用x表示为什么?
∵log(y²)x=log(x²)(y²)/log(x²)x=2log(x²)(y²)=log(x²)(y⁴)∴log(x²)y+log(x²)(y⁴)=1∴log(x²)(y⁴y)=1∴x²=y⁴y∴y=x^(2/5)（即x的2/5次方）设x＞1，y＞1，且2logxy-2logyx+3=0，求T=x2-4y2的最小值．_百度作业帮
设x＞1，y＞1，且2logxy-2logyx+3=0，求T=x2-4y2的最小值．
设x＞1，y＞1，且2logxy-2logyx+3=0，求T=x2-4y2的最小值．
令t=logxy，∵x＞1，y＞1，∴t＞0．由2logxy-2logyx+3=0得，∴2t2+3t-2=0，∴（2t-1）（t+2）=0，∵t＞0，∴，即xy＝12，∴12，∴T=x2-4y2=x2-4x=（x-2）2-4，∵x＞1，∴当x=2时，Tmin=-4．
本题考点：
对数的运算性质；函数的最值及其几何意义．
问题解析：
应用换元法先解出logxy 的值，找出x和y的关系，从而求T=x2-4y2的最小值．Special functions (scipy.special) & SciPy v0.14.0 Reference Guide
Special functions ()
Nearly all of the functions below are universal functions and follow
broadcasting and automatic array-looping rules. Exceptions are noted.
Error handling
Errors are handled by returning nans, or other appropriate values.
Some of the special function routines will emit warnings when an error
By default this is disabled.
To enable such messages use
errprint(1), and to disable such messages use errprint(0).
&&& print scipy.special.bdtr(-1,10,0.3)
&&& scipy.special.errprint(1)
&&& print scipy.special.bdtr(-1,10,0.3)
([inflag])
Sets or returns the error printing flag for special functions.
Available functions
Airy functions
Airy functions and their derivatives.
Exponentially scaled Airy functions and their derivatives.
Compute the zeros of Airy Functions Ai(x) and Ai’(x), a and a’ respectively, and the associated values of Ai(a’) and Ai’(a).
Compute the zeros of Airy Functions Bi(x) and Bi’(x), b and b’ respectively, and the associated values of Ai(b’) and Ai’(b).
Elliptic Functions and Integrals
Jacobian elliptic functions
Computes the complete elliptic integral of the first kind.
The complete elliptic integral of the first kind around m=1.
Incomplete elliptic integral of the first kind
Complete elliptic integral of the second kind
Incomplete elliptic integral of the second kind
Bessel Functions
Bessel function of the first kind of real order v
Bessel function of the first kind of real order v
Exponentially scaled Bessel function of order v
Bessel function of the second kind of integer order
Bessel function of the second kind of real order
Exponentially scaled Bessel function of the second kind of real order
Modified Bessel function of the second kind of integer order n
Modified Bessel function of the second kind of real order v
Exponentially scaled modified Bessel function of the second kind.
Modified Bessel function of the first kind
of real order
Exponentially scaled modified Bessel function of the first kind
Hankel function of the first kind
Exponentially scaled Hankel function of the first kind
Hankel function of the second kind
Exponentially scaled Hankel function of the second kind
The following is not an universal function:
Compute sequence of lambda functions with arbitrary order v and their derivatives.
Zeros of Bessel Functions
These are not universal functions:
Compute nt (&=1200) zeros of the Bessel functions Jn and Jn’ and arange them in order of their magnitudes.
Compute nt zeros of the Bessel functions Jn(x), Jn’(x), Yn(x), and Yn’(x), respectively.
Compute nt zeros of the Bessel function Jn(x).
Compute nt zeros of the Bessel function Jn’(x).
Compute nt zeros of the Bessel function Yn(x).
Compute nt zeros of the Bessel function Yn’(x).
(nt[,&complex])
Returns nt (complex or real) zeros of Y0(z), z0, and the value of Y0’(z0) = -Y1(z0) at each zero.
(nt[,&complex])
Returns nt (complex or real) zeros of Y1(z), z1, and the value of Y1’(z1) = Y0(z1) at each zero.
(nt[,&complex])
Returns nt (complex or real) zeros of Y1’(z), z1’, and the value of Y1(z1’) at each zero.
Faster versions of common Bessel Functions
Bessel function the first kind of order 0
Bessel function of the first kind of order 1
Bessel function of the second kind of order 0
Bessel function of the second kind of order 1
Modified Bessel function of order 0
Exponentially scaled modified Bessel function of order 0.
Modified Bessel function of order 1
Exponentially scaled modified Bessel function of order 0.
Modified Bessel function K of order 0
Exponentially scaled modified Bessel function K of order 0
Modified Bessel function of the first kind of order 1
Exponentially scaled modified Bessel function K of order 1
Integrals of Bessel Functions
Integrals of Bessel functions of order 0
Integrals related to Bessel functions of order 0
Integrals of modified Bessel functions of order 0
Integrals related to modified Bessel functions of order 0
(a,&lmb,&nu)
Weighed integral of a Bessel function.
Derivatives of Bessel Functions
(v,&z[,&n])
Return the nth derivative of Jv(z) with respect to z.
(v,&z[,&n])
Return the nth derivative of Yv(z) with respect to z.
(v,&z[,&n])
Return the nth derivative of Kv(z) with respect to z.
(v,&z[,&n])
Return the nth derivative of Iv(z) with respect to z.
(v,&z[,&n])
Return the nth derivative of H1v(z) with respect to z.
(v,&z[,&n])
Return the nth derivative of H2v(z) with respect to z.
Spherical Bessel Functions
These are not universal functions:
Compute the spherical Bessel function jn(z) and its derivative for all orders up to and including n.
Compute the spherical Bessel function yn(z) and its derivative for all orders up to and including n.
Compute the spherical Bessel functions, jn(z) and yn(z) and their derivatives for all orders up to and including n.
Compute the spherical Bessel function in(z) and its derivative for all orders up to and including n.
Compute the spherical Bessel function kn(z) and its derivative for all orders up to and including n.
Compute the spherical Bessel functions, in(z) and kn(z) and their derivatives for all orders up to and including n.
Riccati-Bessel Functions
These are not universal functions:
Compute the Ricatti-Bessel function of the first kind and its derivative for all orders up to and including n.
Compute the Ricatti-Bessel function of the second kind and its derivative for all orders up to and including n.
Struve Functions
Struve function
Modified Struve function
Integral of the Struve function of order 0
Integral related to Struve function of order 0
Integral of the modified Struve function of order 0
Raw Statistical Functions
: Friendly versions of these functions.
Binomial distribution cumulative distribution function.
Binomial distribution survival function.
Inverse function to bdtr vs.
Cumulative beta distribution.
p-th quantile of the beta distribution.
(dfn,&dfd,&x)
F cumulative distribution function
(dfn,&dfd,&x)
F survival function
(dfn,&dfd,&p)
Inverse to fdtr vs x
Gamma distribution cumulative density function.
Gamma distribution survival function.
(p,&b,&x[,&out])
Inverse of gdtr vs a.
(a,&p,&x[,&out])
Inverse of gdtr vs b.
(a,&b,&p[,&out])
Inverse of gdtr vs x.
Negative binomial cumulative distribution function
Negative binomial survival function
Inverse of nbdtr vs p
Poisson cumulative distribution function
Poisson survival function
Inverse to pdtr vs m
Student t distribution cumulative density function
Inverse of stdtr vs df
Inverse of stdtr vs t
Chi square cumulative distribution function
Chi square survival function
Inverse to chdtrc
Gaussian cumulative distribution function
Inverse of ndtr vs x
Kolmogorov-Smirnov complementary cumulative distribution function
Inverse to smirnov
Complementary cumulative distribution function of Kolmogorov distribution
Inverse function to kolmogorov
(x,&lmbda)
Tukey-Lambda cumulative distribution function
Logit ufunc for ndarrays.
Expit ufunc for ndarrays.
(x,&lmbda)
Compute the Box-Cox transformation.
(x,&lmbda)
Compute the Box-Cox transformation of 1 + x.
Gamma and Related Functions
Gamma function
Logarithm of absolute value of gamma function
Sign of the gamma function.
Incomplete gamma function
Inverse to gammainc
Complemented incomplete gamma integral
Inverse to gammaincc
Beta function.
Natural logarithm of absolute value of beta function.
Incomplete beta integral.
Inverse function to beta integral.
Digamma function
Gamma function inverted
Polygamma function which is the nth derivative of the digamma (psi) function.
Returns the log of multivariate gamma, also sometimes called the generalized gamma.
Error Function and Fresnel Integrals
Returns the error function of complex argument.
Complementary error function, 1 - erf(x).
Scaled complementary error function, exp(x^2) erfc(x).
Imaginary error function, -i erf(i z).
Inverse function for erf
Inverse function for erfc
Faddeeva function
Dawson’s integral.
Fresnel sin and cos integrals
Compute nt complex zeros of the sine and cosine Fresnel integrals S(z) and C(z).
Modified Fresnel positive integrals
Modified Fresnel negative integrals
These are not universal functions:
Compute nt complex zeros of the error function erf(z).
Compute nt complex zeros of the cosine Fresnel integral C(z).
Compute nt complex zeros of the sine Fresnel integral S(z).
Legendre Functions
Associated legendre function of integer order.
Compute spherical harmonics.
These are not universal functions:
(m,&n,&z[,&type])
Associated Legendre function of the first kind, Pmn(z)
Compute sequence of Legendre functions of the first kind (polynomials), Pn(z) and derivatives for all degrees from 0 to n (inclusive).
Compute sequence of Legendre functions of the second kind, Qn(z) and derivatives for all degrees from 0 to n (inclusive).
Associated Legendre function of the first kind, Pmn(z)
Associated Legendre functions of the second kind, Qmn(z) and its derivative, Qmn'(z) of order m and degree n.
Orthogonal polynomials
The following functions evaluate values of orthogonal polynomials:
(n,&x[,&out])
Evaluate Legendre polynomial at a point.
(n,&x[,&out])
Evaluate Chebyshev T polynomial at a point.
(n,&x[,&out])
Evaluate Chebyshev U polynomial at a point.
(n,&x[,&out])
Evaluate Chebyshev C polynomial at a point.
(n,&x[,&out])
Evaluate Chebyshev S polynomial at a point.
(n,&alpha,&beta,&x[,&out])
Evaluate Jacobi polynomial at a point.
(n,&x[,&out])
Evaluate Laguerre polynomial at a point.
(n,&alpha,&x[,&out])
Evaluate generalized Laguerre polynomial at a point.
(n,&x[,&out])
Evaluate Hermite polynomial at a point.
(n,&x[,&out])
Evaluate normalized Hermite polynomial at a point.
(n,&alpha,&x[,&out])
Evaluate Gegenbauer polynomial at a point.
(n,&x[,&out])
Evaluate shifted Legendre polynomial at a point.
(n,&x[,&out])
Evaluate shifted Chebyshev T polynomial at a point.
(n,&x[,&out])
Evaluate shifted Chebyshev U polynomial at a point.
(n,&p,&q,&x[,&out])
Evaluate shifted Jacobi polynomial at a point.
The functions below, in turn, return orthopoly1d objects, which
functions similarly as numpy.poly1d.
The orthopoly1d
class also has an attribute weights which returns the roots, weights,
and total weights for the appropriate form of Gaussian quadrature.
These are returned in an n x 3 array with roots in the first column,
weights in the second column, and total weights in the final column.
(n[,&monic])
Returns the nth order Legendre polynomial, P_n(x), orthogonal over [-1,1] with weight function 1.
(n[,&monic])
Return nth order Chebyshev polynomial of first kind, Tn(x).
(n[,&monic])
Return nth order Chebyshev polynomial of second kind, Un(x).
(n[,&monic])
Return nth order Chebyshev polynomial of first kind, Cn(x).
(n[,&monic])
Return nth order Chebyshev polynomial of second kind, Sn(x).
(n,&alpha,&beta[,&monic])
Returns the nth order Jacobi polynomial, P^(alpha,beta)_n(x) orthogonal over [-1,1] with weighting function (1-x)**alpha (1+x)**beta with alpha,beta & -1.
(n[,&monic])
Return the nth order Laguerre polynoimal, L_n(x), orthogonal over
(n,&alpha[,&monic])
Returns the nth order generalized (associated) Laguerre polynomial,
(n[,&monic])
Return the nth order Hermite polynomial, H_n(x), orthogonal over
(n[,&monic])
Return the nth order normalized Hermite polynomial, He_n(x), orthogonal
(n,&alpha[,&monic])
Return the nth order Gegenbauer (ultraspherical) polynomial,
(n[,&monic])
Returns the nth order shifted Legendre polynomial, P^*_n(x), orthogonal over [0,1] with weighting function 1.
(n[,&monic])
Return nth order shifted Chebyshev polynomial of first kind, Tn(x).
(n[,&monic])
Return nth order shifted Chebyshev polynomial of second kind, Un(x).
(n,&p,&q[,&monic])
Returns the nth order Jacobi polynomial, G_n(p,q,x) orthogonal over [0,1] with weighting function (1-x)**(p-q) (x)**(q-1) with p&q-1 and q & 0.
Large-order polynomials obtained from these functions
are numerically unstable.
orthopoly1d objects are converted to poly1d, when doing
arithmetic.
numpy.poly1d works in power basis and cannot
represent high-order polynomials accurately, which can cause
significant inaccuracy.
Hypergeometric Functions
(a,&b,&c,&z)
Gauss hypergeometric function 2F1(a, z).
Confluent hypergeometric function 1F1(a, x)
Confluent hypergeometric function U(a, b, x) of the second kind
Confluent hypergeometric limit function 0F1.
(a,&b,&x,&type)
Hypergeometric function 2F0 in y and an error estimate
(a,&b,&c,&x)
Hypergeometric function 1F2 and error estimate
(a,&b,&c,&x)
Hypergeometric function 3F0 in y and an error estimate
Parabolic Cylinder Functions
Parabolic cylinder function D
Parabolic cylinder function V
Parabolic cylinder function W
These are not universal functions:
Compute sequence of parabolic cylinder functions Dv(x) and their derivatives for Dv0(x)..Dv(x) with v0=v-int(v).
Compute sequence of parabolic cylinder functions Dv(x) and their derivatives for Dv0(x)..Dv(x) with v0=v-int(v).
Compute sequence of parabolic cylinder functions Dn(z) and their derivatives for D0(z)..Dn(z).
Mathieu and Related Functions
Characteristic value of even Mathieu functions
Characteristic value of odd Mathieu functions
These are not universal functions:
Compute expansion coefficients for even Mathieu functions and modified Mathieu functions.
Compute expansion coefficients for even Mathieu functions and modified Mathieu functions.
The following return both function and first derivative:
Even Mathieu function and its derivative
Odd Mathieu function and its derivative
Even modified Mathieu function of the first kind and its derivative
Even modified Mathieu function of the second kind and its derivative
Odd modified Mathieu function of the first kind and its derivative
Odd modified Mathieu function of the second kind and its derivative
Spheroidal Wave Functions
Prolate spheroidal angular function of the first kind and its derivative
Prolate spheroidal radial function of the first kind and its derivative
Prolate spheroidal radial function of the secon kind and its derivative
(m,&n,&c,&x)
Oblate spheroidal angular function of the first kind and its derivative
Oblate spheroidal radial function of the first kind and its derivative
Oblate spheroidal radial function of the second kind and its derivative.
Characteristic value of prolate spheroidal function
Characteristic value of oblate spheroidal function
Compute a sequence of characteristic values for the prolate spheroidal wave functions for mode m and n’=m..n and spheroidal parameter c.
Compute a sequence of characteristic values for the oblate spheroidal wave functions for mode m and n’=m..n and spheroidal parameter c.
The following functions require pre-computed characteristic value:
(m,n,c,cv,x)
Prolate sheroidal angular function pro_ang1 for precomputed characteristic value
(m,n,c,cv,x)
Prolate sheroidal radial function pro_rad1 for precomputed characteristic value
(m,n,c,cv,x)
Prolate sheroidal radial function pro_rad2 for precomputed characteristic value
(m,&n,&c,&cv,&x)
Oblate sheroidal angular function obl_ang1 for precomputed characteristic value
(m,n,c,cv,x)
Oblate sheroidal radial function obl_rad1 for precomputed characteristic value
(m,n,c,cv,x)
Oblate sheroidal radial function obl_rad2 for precomputed characteristic value
Kelvin Functions
Kelvin functions as complex numbers
Compute nt zeros of all the Kelvin functions returned in a length 8 tuple of arrays of length nt.
Kelvin function ber.
Kelvin function bei
Derivative of the Kelvin function ber
Derivative of the Kelvin function bei
Kelvin function ker
Kelvin function ker
Derivative of the Kelvin function ker
Derivative of the Kelvin function kei
These are not universal functions:
Compute nt zeros of the Kelvin function ber x
Compute nt zeros of the Kelvin function bei x
Compute nt zeros of the Kelvin function ber’ x
Compute nt zeros of the Kelvin function bei’ x
Compute nt zeros of the Kelvin function ker x
Compute nt zeros of the Kelvin function kei x
Compute nt zeros of the Kelvin function ker’ x
Compute nt zeros of the Kelvin function kei’ x
Combinatorics
(N,&k[,&exact,&repetition])
The number of combinations of N things taken k at a time.
(N,&k[,&exact])
Permutations of N things taken k at a time, i.e., k-permutations of N.
Other Special Functions
Binomial coefficient
Exponential integral E_n
Exponential integral E_1 of complex argument z
Exponential integral Ei
(n[,&exact])
The factorial function, n! = special.gamma(n+1).
(n[,&exact])
Double factorial.
(n,&k[,&exact])
= multifactorial of order k
Hyperbolic sine and cosine integrals
Sine and cosine integrals
Dilogarithm integral
(z[,&k,&tol])
Lambert W function [R416].
Hurwitz zeta function
Riemann zeta function minus 1.
Convenience Functions
Cube root of x
Convert from degrees to radians
Cosine of the angle x given in degrees.
Sine of angle given in degrees
Tangent of angle x given in degrees.
Cotangent of the angle x given in degrees.
Calculates log(1+x) for use when x is near zero
exp(x) - 1 for use when x is near zero.
cos(x) - 1 for use when x is near zero.
Round to nearest integer
Compute x*log(y) so that the result is 0 if x = 0.
Compute x*log1p(y) so that the result is 0 if x = 0.0,f’’(X)">
#########!求导!logY=1.9+0.3*logX求导：f’(X) 以及二次导数 f’’(X)如果不好求导 请问是不是 f’(X)>0,f’’(X)_百度作业帮
#########!求导!logY=1.9+0.3*logX求导：f’(X) 以及二次导数 f’’(X)如果不好求导 请问是不是 f’(X)>0,f’’(X)
#########!求导!logY=1.9+0.3*logX求导：f’(X) 以及二次导数 f’’(X)如果不好求导 请问是不是 f’(X)>0,f’’(X)
log Y=1.9+0.3* y=10^(1.9+0.3logx)d(logy)/dx=(1/y)dy/dx0.3d(logx)/dx=0.3/x∴y'/y=0.3/xf '(x)=y'=0.3y/x=(0.3/x)*[10^(1.9+0.3logx)],if x>0,f '(x)>0f "(x)=(-0.3/x^2)*[10^(1.9+0.3logx)]+(0.3/x)*[10^(1.9+0.3logx)]*0.3/x=(-0.21/x^2)*[10^(1.9+0.3logx)]