อนุพันธ์

$y= \frac{4x^2+5}{2+\sqrt{x^2+1}} $

วิธีทำ

\begin{align} & \cssId{Step1}{ \frac{dy}{dx} = \frac{(2+\sqrt{x^2+1}) \frac{d}{dx} (4x^2+5) - (4x^2+5) \frac{d}{dx} (2+\sqrt{x^2+1} )}{(2+\sqrt{x^2+1})^2} } \\ &\cssId{Step2}{ = \frac{(2+\sqrt{x^2+1}) (8x) - (4x^2+5) \frac{1}{2 \sqrt{x^2+1}} (2x) }{(2+\sqrt{x^2+1})^2} } \\ &\cssId{Step3}{ = \frac{(2+\sqrt{x^2+1}) (8x) - (4x^2+5) \frac{x}{ \sqrt{x^2+1}}}{(2+\sqrt{x^2+1})^2} } \\ \end{align}