How do you differentiate #g(x) = (2x^2 + 4x - 3) ( 2x + 2)# using the product rule?

1 Answer
Feb 25, 2016

Answer:

#2(2x^2+4x-3) + 8(x+1)^2#

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)#

let #f(x) =2x^2+4x-3#

#rArr f'(x) = 4x+4 = 4(x+1)#

and let #h(x) = 2x+2 rArr h'(x) = 2#

substitute values back into #g'(x)#

hence #g'(x) = [(2x^2+4x-3)*2 ] + [(2x+2)*4(x+1)]#

#rArr g'(x) = 2(2x^2+4x-3) + 2(x+1)*4(x+1)#

#= 2(2x^2+4x-3) + 8(x+1)^2#

If you like, this can be simplified into a single polynomial expression:

#g'(x)=12x^2+24x+2#