อนุพันธ์(กฎลูกโซ่)

$ y= (\frac{4x^2+5}{x+6})^5 $

วิธีทำ

\begin{align} & \cssId{Step1}{ ให้ u = \frac{4x^2+5}{x+6} } \\ &\cssId{Step2}{ \frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx} } \\ &\cssId{Step3}{ = \frac{d}{du} (u^5) \frac{d}{dx} (\frac{4x^2+5}{x+6}) } \\ &\cssId{Step4}{ = 5 u^4 \quad \frac{(x+6) (8x) - (4x^2+5)}{(x+6)^2} } \\ &\cssId{Step5}{ = 5 (\frac{4x^2+5}{x+6}) ^4 \quad ( \frac{(x+6) (8x) - (4x^2+5)}{(x+6)^2 }) } \\ \end{align}