How do you differentiate f(x)=(2e^x+x)(x-2)f(x)=(2ex+x)(x2) using the product rule?

1 Answer
Apr 1, 2016

2e^x + x + (x-2)(2e^x + 1) 2ex+x+(x2)(2ex+1)

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)