Chain rule with partial derivative

Question

Huy Hoang Huynh Nguyen 2020-8-31

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/586709-chain-rule-with-partial-derivative

评论： Huy Hoang Huynh Nguyen 2020-8-31

Hello,

I need to take partial derivative with chain rule of this function f: f(x,y,z) = y*z/x; x = exp(t); y = log(t); z = t^2 - 1

I tried as shown below but in the end I cannot substitute in order to complete the calculation.

clear
clc
syms x y z t
f = @(x,y,z) y.*z.*x.^(-1)
df_x = diff(f,x)
df_y = diff(f,y)
df_z = diff(f,z)
x = @(t) exp(t);
y = @(t) log(t);
z = @(t) t^2 - 1;
x1 = x(1);
y1 = y(1);
z1 = z(1);
dx_t = diff(x,t)
dy_t = diff(y,t)
dz_t = diff(z,t)
df_t = df_x*dx_t + df_y*+dy_t + df_z*dz_t
df_t1 = subs(df_t,{x,y,z},{x1,y1,z1,1})