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need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.2 question 50

Answers (1)

Answer: 3 e^{-3 x}\left\{\frac{1}{1+x}-3 \log (1+x)\right\}

Hint: you must know the rule of solving exponential and logarithm functions

Given: 3 e^{-3 x} \log (1+x)

Solution:

Let  y=3 e^{-3 x} \log (1+x)

Differentiate with respect to x

\frac{\mathrm{dy}}{\mathrm{dx}}=3 \frac{\mathrm{d}}{\mathrm{dx}}\left[e^{-3 x} \log (1+x)\right]

        \begin{aligned} &=3\left\{e^{-3 x} \frac{1}{(1+x)}+\log (1+x)\left(-3 e^{-3 x}\right)\right\} \\\\ &\Rightarrow 3\left\{\frac{e^{-3 x}}{1+x}-3 e^{-3 x} \log (1+x)\right\} \\\\ &\Rightarrow 3 e^{-3 x}\left\{\frac{1}{1+x}-3 \log (1+x)\right\} \end{aligned}

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