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

##### 1 Answer

Apr 1, 2016

#### Answer:

#### 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) #