อนุพันธ์

$ y= x \arctan ( 1+x^2) - arccot (1-x) $

วิธีทำ

\begin{align} & \cssId{Step1}{ \frac{dy}{dx} = x \frac{d}{dx} \arctan ( 1+x^2) +\arctan ( 1+x^2) \frac{d}{dx} x - \frac{d}{dx} arccot (1-x) } \\ &\cssId{Step2}{= x \frac{1}{1+(1+x^2)^2} \cdot 2x +\arctan ( 1+x^2) - \frac{-1}{1+(1-x)^2} (-1) } \\ &\cssId{Step3}{ = \frac{2x^2}{1+(1+x^2)^2} +\arctan ( 1+x^2) - \frac{1}{1+(1-x)^2}} \\ \end{align}