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Question Number 162280 by MathsFan last updated on 28/Dec/21

$$y=x^{sinx}$$$$find{y}^{\prime }$$

Answered by Ar Brandon last updated on 28/Dec/21

$$y=x^{\sin x}$$$$\ln y=\sin x\ln x$$$$\frac{1}{y}\cdot \frac{dy}{dx}=\frac{\sin x}{x}+\cos x\ln x$$$$\Rightarrow \frac{dy}{dx}=x^{\sin x}(\frac{\sin x}{x}+\cos x\ln x)$$

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