Solve: xsinx

1.	Solve: xsinx
Answer» Let y = x^sinx, taking log^m both sides log y = sinx log x, Diff w.r.t x \(\frac{1}{y}.\frac{dy}{dx}\)= sin x .\(\frac{1}{x}\) + log x . cos x \(\frac{dy}{dx}\) = y[\(\frac{sinx}{x}\) + log x . cos x]

Answer»

Let y = x^sinx, taking log^m both sides

log y = sinx log x, Diff w.r.t x

\(\frac{1}{y}.\frac{dy}{dx}\)= sin x .\(\frac{1}{x}\) + log x . cos x

\(\frac{dy}{dx}\) = y[\(\frac{sinx}{x}\) + log x . cos x]

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