Question

How do you differentiate `f(x)=(x^3+2x)e^x`?

Answer 1

`f'(x)=e^x(x^3+3x^2+2x+2)`

Explanation:

`"differentiate using the "color(blue)"product rule"`

`"given "f(x)=g(x)h(x)" then"`

`f'(x)=g(x)h'(x)+h(x)g'(x)larrcolor(blue)"product rule"`

`g(x)=x^3+2xrArrg'(x)=3x^2+2`

`h(x)=e^xrArrh'(x)=e^x`

`rArrf'(x)=(x^3+2x)e^x+(3x^2+2)e^x`

`color(white)(rArrf'(x))=e^x(x^3+3x^2+2x+2)`