d/(du)(x^2+x{y}(x,u)(x,u)^3)

解

\frac{d}{d u} (x^{2} + x y (x, u) (x, u)^{3})

0 + x (\frac{d}{d u} (y (x, u)) (x, u)^{3} + 3 (x, u)^{2} (x, 1) y (x, u))

解答ステップ

\frac{d}{d u} (x^{2} + x y (x, u) (x, u)^{3})

x

を定数として扱う

和/差の法則を適用:

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

= \frac{d}{d u} (x^{2}) + \frac{d}{d u} (x y (x, u) (x, u)^{3})

\frac{d}{d u} (x^{2}) = 0

\frac{d}{d u} (x y (x, u) (x, u)^{3}) = x (\frac{d}{d u} (y (x, u)) (x, u)^{3} + 3 (x, u)^{2} (x, 1) y (x, u))

= 0 + x (\frac{d}{d u} (y (x, u)) (x, u)^{3} + 3 (x, u)^{2} (x, 1) y (x, u))