Question

三阶偏导数设e的sin(2x+3y)次方,求Z的三阶偏导数是多少?

Answer 1

我用数学软件Matlab帮你做的

>> syms x y

>> z=exp(sin(2*x+3*y));

>> diff(z,x,1)

ans =

2*cos(2*x+3*y)*exp(sin(2*x+3*y))

>> diff(z,x,2)

ans =

-4*sin(2*x+3*y)*exp(sin(2*x+3*y))+4*cos(2*x+3*y)^2*exp(sin(2*x+3*y))

>> diff(z,x,3)

ans =

-8*cos(2*x+3*y)*exp(sin(2*x+3*y))-24*sin(2*x+3*y)*cos(2*x+3*y)*exp(sin(2*x+3*y))+8*cos(2*x+3*y)^3*exp(sin(2*x+3*y))

>> diff(z,y,1)

ans =

3*cos(2*x+3*y)*exp(sin(2*x+3*y))

>> diff(z,y,2)

ans =

-9*sin(2*x+3*y)*exp(sin(2*x+3*y))+9*cos(2*x+3*y)^2*exp(sin(2*x+3*y))

>> diff(z,y,3)

ans =

-27*cos(2*x+3*y)*exp(sin(2*x+3*y))-81*sin(2*x+3*y)*cos(2*x+3*y)*exp(sin(2*x+3*y))+27*cos(2*x+3*y)^3*exp(sin(2*x+3*y))