How do you differentiate f(x)=(2e^x+x)(x-2)f(x)=(2ex+x)(x−2) using the product rule?
1 Answer
Apr 1, 2016
Explanation:
Differentiate using the
color(blue)" product rule " product rule If f(x) = g(x).h(x) then f'(x) = g(x).h'(x) + h(x).g'(x)
the standard derivative :
d/dx(e^x) = e^x ddx(ex)=ex
" ----------------------------------------------------" ---------------------------------------------------- g(x) =
2e^x + x rArr g'(x) = 2e^x + 1 and h(x) = x - 2
rArr h'(x) = 1
" -------------------------------------------------" Substituting these values into f'(x)
rArr f'(x) = 2e^x + x + (x-2)(2e^x + 1)