Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferentiation3 Marks
Question
Differentiate the following functions with respect to x: $\sin(\log\sin\text{x})$
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Answer
Consider $\text{y}=\sin(\log\sin\text{x})$ Differentiate with respect to x, $\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\sin(\log\sin\text{x})$ $=\cos(\log\sin\text{x})\frac{\text{d}}{\text{dx}}(\log\sin\text{x})$ [Using chain rule] $=\cos(\log\sin\text{x})\times\frac{1}{\sin\text{x}}\frac{\text{d}}{\text{dx}}0\sin\text{x}$ $=\cos(\log\sin\text{x})\frac{\cos\text{x}}{\sin\text{x}}$ $=\cos(\log\sin\text{x})\times\cot\text{x}$ Hence, the solution is, $\frac{\text{d}}{\text{dx}}(\sin(\log\sin\text{x}))=\cos(\log\sin\text{x})\text{x}\cot\text{x}$
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