subs in symbolic equation

Hello.

I have calculated a partial derivative of a function as following:

clear

clc

syms x y r t real

f = @(r,t) r.*cos(t);

df_r = diff(f,r);

df_t = diff(f,t);

r = @(x,y) sqrt(x.^2 + y.^2);

dr_x = diff(r,x);

t = @(x,y) atan(y,x);

dt_x = diff(t,x);

df_x = df_r*dr_x + df_t*dt_x

the result is :

df_x =

(x*cos(t))/(x^2 + y^2)^(1/2) + (r*y*sin(t))/(x^2 + y^2)

How can I get the df_x in only r and t. I would like to substititute x^2+y^2 with r^2, x with r*cos(t) and y with r*sin(t).

Thanks

Answer 1

[Hrishikesh Borate]

Hi,

It’s my understanding that you are trying to obtain df_x in terms of r and t. Following addition to the existing code will do the same:-

syms r t
df_x = subs(df_x, x.^2+y.^2, r.^2);
df_x = subs(df_x, [x,y], [r*cos(t),r*sin(t)]);

For more information refer to subs.