Question

Use logarithmic differentiation to find the derivative of the function y = x^(sin x)

Answer 1

\[\ln (y) = \sin x *\ln(x)\]
differentiate
\[\frac{y'}{y} = \frac{\sin x}{x}+\cos x \ln(x)\]
\[y' = y \frac{\sin x}{x}+y \cos x \ln(x)\]