# Partial Derivative

• Nov 24th 2007, 03:12 PM
brd_7
Partial Derivative
Ive got these two questions, and im not too sure how to solve them.. Any help would be appreciated.. Thanks in Advance.

Find \frac{\partial w}{\partial x} and \frac{\partial w}{\partial y} for

w = ucosv, u = x^2 + y^3 and v = x^3 y^2
• Nov 24th 2007, 04:02 PM
kalagota
Quote:

Originally Posted by brd_7
Ive got these two questions, and im not too sure how to solve them.. Any help would be appreciated.. Thanks in Advance.

Find \frac{\partial w}{\partial x} and \frac{\partial w}{\partial y} for

w = ucosv, u = x^2 + y^3 and v = x^3 y^2

$\frac{\partial w}{\partial x} = \frac{\partial w}{\partial u}\frac{\partial u}{\partial x} + \frac{\partial w}{\partial v}\frac{\partial v}{\partial x} = (\cos v)(2x) + -u (\sin v)3x^2y^2$.. substitute the values of u and v..

do for the second one..

$\frac{\partial w}{\partial y} = \frac{\partial w}{\partial u}\frac{\partial u}{\partial y} + \frac{\partial w}{\partial v}\frac{\partial v}{\partial y}$