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

1 Answer
Mar 10, 2016

Answer:

#(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)#