Question

FInd the derivative of each of the following function.

f(x)=xcosx+x^4e^2x

All I know is the rule with the e^u equation where you would do e^2x times 1. other than that I dont know what to do can someone please help and show all work I will appreciate it greatly

Answer 1

f' = x d/dx(cos x) + cos x dx/dx +x^4d/dx(e^2x) + e^2x d/dx(x^4)

= -x sin x + cos x + 2x^4(e^2x) + 4x^3 (e^2x)

Answer 2

just the good old chain rule and product rule

d/dx e^u = e^u du/dx
d/dx uv = u'v + uv'

so, with

y = x cosx + x^4 e^2x
y' = (1)cosx + (x)(-sinx) + (4x^3)(e^2x) + (x^4)(e^2x)(2)