อนุพันธ์

$ y= \frac{\ln| x+2| }{2+x+e^{4x}} $

วิธีทำ

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