Differentiate:

Question

F(x)=e^(xsin2x)

This isn't homework, it's review for our exam. Couldn't remember how to work it :( Thanks!

Answer 1

Several layers of derivatives here ...
remember for y = e^u
dy/dx = e^u (du/dx)

so f'(x) = e^(xsin2x)(d(xsin2x)/dx)
= e^(xsin2x)(x(2cos2x) + sin2x) using the product rule for the last part

Answer 2

Thank you! :)