# Partial Derivatives

• Mar 22nd 2011, 01:59 PM
bilalsaeedkhan
Partial Derivatives
How do I find the first partials of the function below?

$f(x,y)=\int_{y}^{x}cos(t^{2})dt$
• Mar 22nd 2011, 02:18 PM
TheEmptySet
Quote:

Originally Posted by bilalsaeedkhan
How do I find the first partials of the function below?

$f(x,y)=\int_{y}^{x}cos(t^{2})dt$

You need to use the fundamental theorem of calculus.

$\displaystyle \frac{\partial f}{\partial y}=\frac{\partial }{\partial y}\left(-\int_{x}^{y}cos(t^{2})dt\right) =-\cos(y^2)$

now try the x one.