Mathematics

Problem

The function

y=\bigl(x\cos x\bigr)^{\tan x}

is defined for

x\in\bigl(0,\tfrac{\pi}{2}\bigr)

. (i) Show that

y

is differentiable on its domain and obtain

\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=\dfrac{\pi}{4}