derivative of (1-x^2+10(y-x^2)^2)

解

\frac{d}{d x} ((1 - x)^{2} + 10 (y - x^{2})^{2})

- 2 (1 - x) + 20 (y - x^{2}) (\frac{d y}{d x} - 2 x)

解答ステップ

\frac{d}{d x} ((1 - x)^{2} + 10 (y - x^{2})^{2})

和/差の法則を適用:

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

= \frac{d}{d x} ((1 - x)^{2}) + \frac{d}{d x} (10 (y - x^{2})^{2})

\frac{d}{d x} ((1 - x)^{2}) = - 2 (1 - x)

\frac{d}{d x} (10 (y - x^{2})^{2}) = 20 (y - x^{2}) (\frac{d y}{d x} - 2 x)

= - 2 (1 - x) + 20 (y - x^{2}) (\frac{d y}{d x} - 2 x)