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

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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