How do you differentiate #(3x+4)^2(4x-1)^3# using the power chain rule?

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Answer 1 · 2018-04-26T13:31:10

#(3x+4)^2*12(4x-1)^2 + (4x-1)^3*(18x+24)#

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

Let

#f(x)=(3x+4)^2# and #g(x) = (4x-1)^3#

The chain rule formula says

#f(x)*g'(x) + g(x)*f'(x)#

#g'(x)=3(4x-1)^2 (4)# and #f'(x)=2(3x+4)(3)#

Simplifying a little, we get

#g'(x)=12(4x-1)^2# and #f'(x)=6(3x+4)=18x+24#

Plugging these back into the chain rule formula above

#(3x+4)^2*12(4x-1)^2 + (4x-1)^3*(18x+24)#

You can continue to simplify this result if you desire, but this is as good a stopping point as any in my opinion.