derivative of 2x+2y(dy/(dx))

解

\frac{d}{d x} (2 x + 2 y \frac{d y}{d x})

2 + 2 (\frac{d y}{d x}^{2} + \frac{d ^{2} y}{d x ^{2}} y)

解答ステップ

\frac{d}{d x} (2 x + 2 y \frac{d y}{d x})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x) + \frac{d}{d x} (2 y \frac{d y}{d x})

\frac{d}{d x} (2 x) = 2

\frac{d}{d x} (2 y \frac{d y}{d x}) = 2 (\frac{d y}{d x}^{2} + \frac{d ^{2} y}{d x ^{2}} y)

= 2 + 2 (\frac{d y}{d x}^{2} + \frac{d ^{2} y}{d x ^{2}} y)