Question

The derivative of tan-¹ x w.r.t. (1 + x²)​

Answer 1

Step-by-step explanation:

$let \: \: u = \tan ^{ - 1} (x) \: \: and \: \: v = 1 + {x}^{2}$

$\implies \frac{du}{dx} = \frac{1}{1 + {x}^{2} } \: \: and \: \: \frac{dv}{dx} = 2x$

$\implies \frac{du}{dv} = \frac{1}{2x(1 + {x}^{2} )}$