How do you differentiate #f(x)=3x(2x+1)^3 # using the product rule?

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Answer 1 · 2018-04-15T02:36:43

#=>f'(x) = 3(2x+1)^2(8x+1)#

#f(x) = 3x(2x+1)^3#

#f'(x) = d/(dx)[3x] (2x+1)^3 + 3xd/(dx)[(2x+1)^3]#

#f'(x) = 3 (2x+1)^3 + 3x(3)(2)(2x+1)^2#

#=>f'(x) = 3 (2x+1)^3 + 18x(2x+1)^2#

If you wish to simplify at all, there is some factoring:

#f'(x) = 3(2x+1)^2[(2x+1)+6x]#

#=>f'(x) = 3(2x+1)^2(8x+1)#