อนุพันธ์

$ y= (5+sin(x))^{(3x^2+1)} $

วิธีทำ

\begin{align} & \cssId{Step1}{ take \quad \ln \quad จะได้ \quad \ln y= (3x^2+1) \ln (5+\sin x ) } \\ &\cssId{Step2}{ดังนั้น \quad \frac{1}{y} \frac{dy}{dx} = (3x^2+1) \frac{d}{dx} \ln (5+\sin x ) + \ln (5+\sin x ) \frac{d}{dx} (3x^2+1) } \\ &\cssId{Step3}{ = (3x^2+1) \frac{1}{5+ \sin x} (\cos x ) + \ln (5+\sin x ) (6x) } \\ &\cssId{Step4}{ ดังนั้น \quad \frac{dy}{dx} = y ( \frac{ (3x^2+1) \cos x }{5+ \sin x} + 6x \ln (5+\sin x ) ) } \\ &\cssId{Step5}{ = (5+sin(x))^{(3x^2+1)} ( \frac{ (3x^2+1) \cos x }{5+ \sin x} + 6x \ln (5+\sin x ) ) } \\ \end{align}