Question

How do you differentiate `f(x)=(cosx+1)(-x^2-3e^x)` using the product rule?

Answer 1

`(cosx + 1 )(-2x-3e^x) - sinx(x^2-3e^x)`

Explanation:

using the `color(blue)" Product rule "`

If f(x) = g(x).h(x) then f'(x) = g(x).h'(x) + h(x).g'(x)

`"----------------------------------------------------------------"`

here g(x) `= cosx + 1 rArr g'(x) = -sinx`

and `h(x) = (-x^2-3e^x) rArr h'(x) = -2x-3e^x`
`"-----------------------------------------------------------------"`

now substitute these results into f'(x)

f'(x) `=(cosx+1)(-2x-3e^x)-sinx(x^2-3e^x)`