d/(dy)((x)(y+(x^2y)h-2x*h-n))

解

\frac{d}{d y} ((x) (y + (x^{2} \cdot y) \cdot h - 2 x \cdot h - n))

x (x^{2} h + 1)

解答ステップ

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

n, x, h

を定数として扱う

定数を除去:

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

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

和/差の法則を適用:

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

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

\frac{d y}{d y} = 1

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

\frac{d}{d y} (2 x h) = 0

\frac{d n}{d y} = 0

= x (1 + x^{2} h - 0 - 0)

簡素化

= x (x^{2} h + 1)