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

1 Answer
Mar 10, 2016

(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)

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

and h(x) = (-x^2-3e^x) rArr h'(x) = -2x-3e^x
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now substitute these results into f'(x)

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