d/dx x^2 * e^(x^5+1)^10

Question

Calculus question. Can you please guide me through how to get the answer? I tried a dozen times but every time I mess up somewhere along the way. I know that I need to use the product rule and chain rule.

Answer 1

You are correct to use the product rule and the chain rule.  The complicated part is in applying the chain rule correctly when differentiating e^(x^5+1)^10.  It is easy to make a mistake.  Here is my attempt at the whole derivative.  Do you have an answer in the book that we can compare against?

 

dy/dx = 2x[e^(x^5+1)^10] + x² [e^(x^5+1)^10] [10(x⁵ + 1)⁹] [5x⁴]