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Find the derivative of   \cot ^{-1}\left(1+x^2\right) with respect to  \left(5 x^2+2 x+1\right)

Option: 1

\frac{2 x}{(5 x+10)\left(x^4+2 x^2+2\right)}


Option: 2

-\frac{2 x}{(10 x+2)\left(x^4+2 x^2+2\right)}


Option: 3

\frac{2 x}{(10 x+2)\left(x^4+2 x^2+2\right)}


Option: 4

-\frac{2 x}{(10 x+2)\left(x^5+2 x^2+2\right)}


Answers (1)

best_answer

Let ,f(x)=\cot ^{-1}\left(1+x^2\right)

Now differentiate with respect to “x”

, f^{\prime}(x)=-\frac{2 x}{2+2 x^2+x^4}

also get   ,g(x)=\left(5 x^2+2 x+1\right)

Now differentiate with respect to “x”


\begin{aligned} & g^{\prime}(x)=10 x+2 \\ & \frac{f^{\prime}(x)}{g^{\prime}(x)}=-\frac{2 x}{(10 x+2)\left(x^4+2 x^2+2\right)} \end{aligned}

Posted by

manish painkra

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