Partial Derivative of a Definite Integral

[jenn9580]

I have just learned about partial derivatives but there is a problem thrown in my homework which isn't covered in the text. I am trying to find the first partial derivative of the function. Could someone explain this? Here is one of the problems. If it were explained, I think I could figure out the answer. Thanks in advance!

 

[BigGlenntheHeavy]

\(\displaystyle f(x,y) \ = \ \int_{y}^{x}cos(t^{3})dt, \ f_x(x,y) \ = \ cos(x^{3}), \ y \ is \ a \ constant.\)

\(\displaystyle f(x,y) \ = \ \int_{x}^{y}-cos(t^{3})dt, \ f_y(x,y) \ = \ -cos(y^{3}), \ x \ is \ a \ constant.\)

 

[jenn9580]

Thank you! I figured it was something along those lines.