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  • Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question 22

Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question  22

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Answer: the correct answer is \frac{3 x^{2}}{1+x^{6}}

Hint: integrate the function.

Given: \frac{d}{\mathrm{dx}} f(x)=\frac{1}{1+x^{2}}

Solution: integrating we get

\begin{aligned} &\int \frac{d}{d x}(f(x)) d x=\int\left[\frac{1}{1+x^{2}}\right] d x \\\\ &f(x)=\tan ^{-1} x+e \end{aligned}

\begin{aligned} &f\left(x^{3}\right)=\tan ^{-1}\left(x^{3}\right)+c \\\\ &f^{1}\left(x^{3}\right)=\frac{3 x^{2}}{1+x^{6}} \end{aligned}

So the answer is  \frac{3 x^{2}}{1+x^{6}}

 

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