I am reviewing some concepts and I do not remember the proper way solve this problem.

I need to differentiate f with respect to x and with respect to y (partial derivatives) for:

f(x,y) = ln(x^5+xy+(y^3)(e^x))

My guess is that f with respect to x is:

(5x^4+y+(y^3)(e^x))((1/ (x^5+xy+(y^3)(e^x)))

But I am pretty sure that my guess is not correct. Can anyone help me with this, please?