How do you differentiate #f(x)= (2x+1)(3x+1)^4 # using the product rule?

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Answer 1 · 2015-12-12T14:15:03

#f'(x)=2(3x+1)^3(15x+7)#

#f'(x)=(3x+1)^4d/dx[2x+1]+(2x+1)d/dx[(3x+1)^4]#

Find each derivative separately.

#d/dx[2x+1]=2#

The following requires chain rule.

#d/dx(3x+1)^4=4(3x+1)^3overbrace(d/dx[3x+1])^(=3)=12(3x+1)^3#

Plug these back in.

#f'(x)=2(3x+1)^4+12(3x+1)^3(2x+1)#

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

#f'(x)=2(3x+1)^3(15x+7)#