Partial derivatives of f(p)/p where p=√(x²+y²+z²)

[hellsingfan]

Homework Statement

Taking the derivative of f(p)/p with respect to x,y,z separately. p = √(x^2+y^2+z^2) while f(p) is a scalar function that we don't know about

Homework Equations

f(p)/p

The Attempt at a Solution

I just wanted to know if the following is a legitimate way of doing it:

for partial derivative with respect to x: (f'(p)*p_xp-f(p)*p_x)/p²

Similarly for derivative with respect to y: (f'(p)*p_yp-f(p)*p_y)/p²

or is putting f'(p)*p_x invalid (i was thinking take the derivative of outside multiply by derivative of inside, but I'm not sure if the chain rule can be applied the way I did)

 

[Dick]

Homework Statement

Taking the derivative of f(p)/p with respect to x,y,z separately. p = √(x^2+y^2+z^2) while f(p) is a scalar function that we don't know about

Homework Equations

f(p)/p

The Attempt at a Solution

I just wanted to know if the following is a legitimate way of doing it:

for partial derivative with respect to x: (f'(p)*p_xp-f(p)*p_x)/p²

Similarly for derivative with respect to y: (f'(p)*p_yp-f(p)*p_y)/p²

or is putting f'(p)*p_x invalid (i was thinking take the derivative of outside multiply by derivative of inside, but I'm not sure if the chain rule can be applied the way I did)

Looks fine so far.