What are the first partial derivatives of a definite integral function?

[icosane]

Homework Statement

Find the first partial derivatives of the function.

f(x,y) = definite integral (limits of integration x to y) cos(t^2) dt

The Attempt at a Solution

Is the partial derivative with respect to x just cos(x^2), and for y, cos(y^2) ? Or should the partial derivative with respect to y be negative?

 

[Dick]

Sure. -cos(y)^2 for the y derivative. That's what the Leibniz rule says, right?