How do you differentiate #g(x) = (5x-2)(x^2+1)# using the product rule?
1 Answer
Feb 6, 2016
# g'(x) = 2x(5x - 2 ) + 5(x^2 + 1 )#
Explanation:
differentiation using the product rule
If g(x) = f(x).h(x)
then g'(x) = f(x).h'(x) + h(x).f'(x)................(A)
here f(x) =(5x - 2 ) and f'(x) = 5
#color(black)("-------------------------------------")# h(x)
# = (x^2 + 1) # hence h'(x) = 2x
#color(black)("--------------------------------")# substituting these values into (A)
g'(x) = (5x - 2).2x +
# (x^2 + 1 ).5#
# rArr g'(x) = 2x(5x - 2) + 5(x^2 + 1 )#
