MathematicsDerivative of cot-1x with respect to tan-11x is

Derivative of $\cot^{- 1} x$ with respect to $\tan^{- 1} (\frac{1}{x})$ is

Solution:

Suppose that $f (x) = c o t^{- 1} x, g (x) = \tan^{- 1} (\frac{1}{x})$

The derivative of $f (x)$ with respect to $g (x)$ is $\begin{array}{rcl} \frac{f' (x)}{g' (x)} \end{array}$

$\begin{array}{rcl} \frac{f' (x)}{g' (x)} & = & - \frac{1}{1 + x^{2}} \cdot \frac{1 + \frac{1}{x^{2}}}{1} (- \frac{1}{x^{2}}) \\ = & 1 \end{array}$

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