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

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

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Answer 1 · 2016-07-21T17:45:22

#d/dx (f(x)) = d/dx ((2x+3)^4/x)#
Or, #f'(x) = 1/x * d/(d(2x+3)) (2x+3)^4* d/dx (2x+3) + (2x+3)^4 d/dx (1/x)#
#=1/x * 4 (2x+3)^3 * 2- (2x+3)^4/x^2#
#=(8x (2x+3)^3-(2x+3)^4)/x^2#
#=(2x+3)^3(8x-2x-3)/x^2#
#= 3 (2x+3)^3 * (2x -1) / x^2#

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

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