AP Calculus AB · Composite, implicit, and inverse-function differentiation
For 0<x<π, let y=(sin x)^x
Problem
For \(0<x<\pi\), let \(y=(\sin x)^{x}\). (a) Use logarithmic differentiation to find \(\dfrac{dy}{dx}\). (b) Find \(y\bigl(\frac{\pi}{2}\bigr)\) and \(y'\bigl(\frac{\pi}{2}\bigr)\). (c) Find an equation of the tangent line to the graph at \(x=\frac{\pi}{2}\).
Hint
Same pattern as \(x^{\cos x}\): log first, because the exponent is variable.
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