JEE MainMathematicsModerateDifferentiation

If $y = \log_{\sqrt{e}}(sinx)$ , then $\frac{dy}{dx}$ is.

Show answer and solution

y = \frac{1}{\frac{1}{2}}\log_{e}\left( \sin x \right) = 2\ln\left( \sin x \right)

\frac{dy}{dx} = 2\frac{cosx}{sinx} = 2cotx

Source: Grass-G / M-19 Mathematics Paper 28 Nov Fourth.docx

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