Question

What is the derivative of `f(x) = (x^5)*(e^x)`?

Answer 1

`(5+x)x^4*e^x`

Explanation:

`f(x)=x^5*e^x`
Product rule states: `d/dxu(x)*v(x)=u'(x)*v(x)+u(x)*v'(x)`
in this case `u(x)=x^5` ; `v(x)=e^x`
`d/dx(f(x))=5x^4*e^x+x^5*e^x` note that `d/dx(e^x)=e^x`
thsi can be simplified by factorisation to `f'(x)=(5+x)x^4*e^x`