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  • Find the second order derivatives of the functions given in Exercises 1 to 10. tan^ -1 x

 Q8  Find the second order derivatives of the functions given in Exercises 1 to 10. 

        \tan ^{-1} x

 

Answers (1)

best_answer

Given function is
y = \tan^{-1}x
Now, differentiation w.r.t. x
\frac{dy}{dx}=\frac{d(\tan^{-1}x)}{dx}=\frac{1}{1+x^2}
Now, second order derivative is
\frac{d^2y}{dx^2}= \frac{-1}{(1+x^2)^2}.2x = \frac{-2x}{(1+x^2)^2}
Therefore,  second order derivative is \frac{d^2y}{dx^2} = \frac{-2x}{(1+x^2)^2}

Posted by

Gautam harsolia

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