Derive a simplified expression for if

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Derive a simplified expression for f′(x)f'(x) if f(x)=(x2+1)tan⁡x (x2+x+1)12cos⁡xf(x) = (x^{2}+1)^{\tan x}\,(x^{2}+x+1)^{\frac{1}{2}\cos x}. Present your result with no remaining logarithms.

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