# Partial derivatives

1. Feb 18, 2006

### UrbanXrisis

sin(5x-4y+z)=0

how do I find $$\frac{\partial z}{\partial x}$$?

if the problem is sin(5x-4y+z)=f(x,y,z), I can find $$\frac{\partial f}{\partial x}$$ but I dont know what to do when it is just equal to zero.

2. Feb 18, 2006

### dicerandom

Solve for z, take the partial derivative.

3. Feb 18, 2006

### HallsofIvy

Staff Emeritus
Simpler: take the partial derivative with respect to x, assuming that y is independent of x, z a function of x, then solve for zx. Use the chain rule. Remember "implicit differentiation" from Calculus I?
(sin(5x- 4y+ z))x= cos(5x- 4y+ z)(5- zx)= 0. Solve for zx.

4. Feb 18, 2006

### dicerandom

HallsofIvy: I think that should be a (5+zx) in your second expression.