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Question Number 146046 by mathdanisur last updated on 10/Jul/21

$$f\left(x\right)=x^{\mathit{s}\mathit{i}\mathit{n}\left(\mathit{x}\right)}\Rightarrow f{}^{{}^{\prime }}\left(x\right)=?$$

Answered by liberty last updated on 10/Jul/21

$$\ln f\left(x\right)=\sin x.\ln \left(x\right)$$$$\iff \frac{f{}^{\prime }\left(x\right)}{f\left(x\right)}=\cos x.\ln \left(x\right)+\frac{\sin x}{x}$$$$\iff f{}^{\prime }\left(x\right)=x^{\sin x}(\cos x.\ln \left(x\right)+\frac{\sin x}{x})$$

Commented by mathdanisur last updated on 10/Jul/21

$$thankyouSer$$

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