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

1 Answer
Mar 5, 2016

e^(3x)(15x - 1 )

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 )