How to find the gradient of a function in spherical coordinates system ?

For example a scalar field in Cartesian coordinates system A=x^2*y+x*y*z So, if we differentiate this entire equation with respect to x, y and z and add them then we will get the answer 3*X*y+x*z+y*z+x^2. But when we calculate the gradient the correct value should be (2*x*y+y*z)ax+(x^2+X*z)ay+(x*y)az

So can anybody please tell me the proper and correct method to find the gradient in spherical coordinates system

Answer 1

[Stephan]

Hi,

take advantage of the gradient function:

syms x y z
A = x^2*y+x*y*z
res = gradient(A,[x y z])

results in:

res =
 
 2*x*y + y*z
   x^2 + z*x
         x*y

Best regards

Stephan