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  4. If y= tan-1 ((x-a/1+xa)) then (dy/dx) =

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Q. If $ y= tan^{-1} \left(\frac{x-a}{1+xa}\right) $ then $ \frac{dy}{dx} = $

J & K CETJ & K CET 2017Continuity and Differentiability

Solution:

We have,
$y=tan^{-1} \left(\frac{x-a}{1+ax}\right)$
$\Rightarrow y=tan^{-1}x-tan^{-1}a $
Differentiating w.r.t. x, we get
$\frac{dy}{dx}=\frac{1}{1+x^{2}}-0$
$=\frac{1}{1+x^{2}}$