# Homework Help: Unusual partial differentiation equation

1. Oct 22, 2012

### rachibabes

1. The problem statement, all variables and given/known data

Calculate ∂f/∂x and ∂f/∂y for the following function:

$yf^2 + sin(xy) = f$

3. The attempt at a solution

I understand basic partial differentiation, but I have no idea how to approach the f incorporation on both sides of the equation nor what you would explicitly call this kind of mathematical technique. Anyone who can point me in the right direction?

2. Oct 22, 2012

### tiny-tim

welcome to pf!

hi rachibabes! welcome to pf!
just do ∂/∂x to the equation in the usual way (using the product rule for the yf2) …

what do you get?

3. Oct 23, 2012

### rachibabes

$yf^2 + sin(xy) = f$

I get:

$y2f∂f/∂x +f^2∂y/∂x + cos(xy)*(x∂y/∂x+y) = ∂f/∂x$

$y2f∂f/∂x +f^2∂y/∂x + x∂y/∂xcos(xy) + ycos(xy) = ∂f/∂x$

$∂y/∂x[f^2 + cos(xy)] + ycos(xy) + y2f∂f/∂x = ∂f/∂x$

I have no idea how to remove the ∂f/∂x on the left hand side :/

4. Oct 23, 2012

### tiny-tim

hey there, rachibabes!

(just got up :zzz:)

f(x,y) is a function of the variables x and y

∂/∂x means differentiating wrt x keeping y fixed

so ∂y/∂x = … ?