How do you differentiate #f(x)=cot(e^{4x})# using the chain rule.?

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Answer 1 · 2015-12-27T06:12:00

#f'(x) = -4csc^2(e^{4x})*e^{4x}#

#f'(x) = frac{d}{dx}( cot(e^{4x}) )#

Let #u = e^{4x}#.

#frac{du}{dx} = 4 e^{4x}#

#frac{d}{dx}( cot(e^{4x}) ) = frac{d}{dx}( cot(u) )#

#= frac{d}{du}( cot(u) )*frac{du}{dx}#

#= -csc^2(u)*(4e^{4x})#

#= -4csc^2(e^{4x})*e^{4x}#