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  • Please solve RD Sharma class 12 chapter Differentiation exercise 10.2 question 44 maths textbook solution

Please solve RD Sharma class 12 chapter Differentiation exercise 10.2 question 44 maths textbook solution

Answers (1)

Answer:  2 e^{x} \cot 2 x+e^{x} \log \sin 2 x

Hint: you must know about the rules of solving derivative of exponential logarithm and trigon function

Given: e^{x} \log \sin 2 x

Solution:

Let  y=e^{x} \log \sin 2 x

Differentiate with respect to x

\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\mathrm{dx}}\left[e^{x} \log \sin 2 x\right]

\begin{aligned} &=e^{x} \frac{\mathrm{d}}{\mathrm{dx}}(\log \sin 2 x)+(\log \sin 2 x) \frac{\mathrm{d}}{\mathrm{dx}}\left(e^{x}\right) \\\\ &=e^{x} \frac{1}{\sin 2 x} \frac{\mathrm{d}}{\mathrm{dx}} \sin 2 x+\log \sin 2 x\left(e^{x}\right) \end{aligned}

\begin{aligned} &=\frac{e^{x}}{\sin 2 x} \cos 2 x \frac{\mathrm{d}}{\mathrm{dx}}(2 x)+e^{x} \log \sin 2 x \\\\ &=\frac{2 \cos 2 x e^{x}}{\sin 2 x}+e^{x} \log \sin 2 x \\\\ &\Rightarrow 2 e^{x} \cot 2 x+e^{x} \log \sin 2 x \end{aligned}

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