How do I differentiate f(x)= yx?

Properly, you’d have to use the product rule. df/dx = y + xdy/dx. If y is independent of x, then dy/dx is 0, and df/dx = y.

The concept you’re looking for is a “partial derivative”. If you google on that, you’ll find lots of info.

How would I integrate it?

Again, if y is independent of x, the integral is yx[sup]2[/sup]/2 + c. If not, you have to integrate by parts.