# How do you differentiate #g(x) = e^(3x) ( 5x-2)# using the product rule?

##### 1 Answer

Mar 5, 2016

#### Answer:

#### Explanation:

differentiate using the

#color(blue)" Product rule "# If g(x) = f(x).h(x) then g'(x) = f(x).h'(x) + h(x).f'(x)

here

# f(x) = e^(3x) rArr f'(x) =e^(3x) d/dx(3x) = 3e^(3x)# and h(x) = (5x - 2 )

# rArr h'(x) = 5# substitute these results into g'(x) above

#g'(x) = 5e^(3x) + 3e^(3x) (5x - 2 )# take out common factor of

# e^(3x) #

#rArr g'(x) = e^(3x)(5+15x - 6 ) = e^(3x)(15x - 1 )#