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

1 Answer
Apr 1, 2016

Answer:

#2e^x + x + (x-2)(2e^x + 1) #

Explanation:

Differentiate using the #color(blue)" 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 #
#" ----------------------------------------------------"#

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) #