The function is defined for

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

Problem

The function y=(xcos⁡x)tan⁡xy=\bigl(x\cos x\bigr)^{\tan x} is defined for x∈(0,π2)x\in\bigl(0,\tfrac{\pi}{2}\bigr). (i) Show that yy is differentiable on its domain and obtain dydx\dfrac{dy}{dx}. (ii) Using the derivative found in part (i), write the equation of the tangent to the curve at the point where x=π4x=\dfrac{\pi}{4}.

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