d/(d{y)}(({z}(x))({x}{y}+sin({x}{y})+{x}))

解

\frac{d}{d y} ((z (x)) (x y + sin (x y) + x))

z (x) (x + cos (x y) x + \frac{d}{d y} (x))

解答ステップ

\frac{d}{d y} ((z (x)) (x y + sin (x y) + x))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= z (x) \frac{d}{d y} (x y + sin (x y) + x)

和/差の法則を適用:

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

= z (x) (\frac{d}{d y} (x y) + \frac{d}{d y} (sin (x y)) + \frac{d}{d y} (x))

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

\frac{d}{d y} (sin (x y)) = cos (x y) x

= z (x) (x + cos (x y) x + \frac{d}{d y} (x))