อนุพันธ์

$y = x \arctan (1 + x^{2}) - a r c c o t (1 - x)$

วิธีทำ

$\begin{aligned} \frac{d y}{d x} = x \frac{d}{d x} \arctan (1 + x^{2}) + \arctan (1 + x^{2}) \frac{d}{d x} x - \frac{d}{d x} a r c c o t (1 - x) \\ = x \frac{1}{1 + (1 + x^{2})^{2}} \cdot 2 x + \arctan (1 + x^{2}) - \frac{- 1}{1 + (1 - x)^{2}} (- 1) \\ = \frac{2 x^{2}}{1 + (1 + x^{2})^{2}} + \arctan (1 + x^{2}) - \frac{1}{1 + (1 - x)^{2}} \end{aligned}$