Derivative of f(x)=etan−1x with respect to g(x)=tan−1x is

Derivative of $f (x) = e^{\tan^{- 1} x}$ with respect to $g (x) = \tan^{- 1} x$ is

A
$g^{1} (x)$
B
$f^{1} (x)$
C
$g (x)$
D
$f (x)$

Solution:

$f^{1} (x) = e^{\tan^{- 1} x} . \frac{1}{1 + x^{2}}, g^{1} (x) = \frac{1}{1 + x^{2}}$

$\frac{f^{1} (x)}{g^{1} (x)} = \frac{e^{\tan^{- 1} x} . \frac{1}{1 + x^{2}}}{\frac{1}{1 + x^{2}}} = e^{\tan^{- 1} x} = f (x)$

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