derivative-7hx^2-5hx-3h^2x+5h^2+4h^3

解

導関数

- 7 h x^{2} - 5 h x - 3 h^{2} x + 5 h^{2} + 4 h^{3}

- 7 x^{2} - 5 x - 6 x h + 10 h + 12 h^{2}

解答ステップ

\frac{d}{d h} (- 7 h x^{2} - 5 h x - 3 h^{2} x + 5 h^{2} + 4 h^{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 h} (7 h x^{2}) - \frac{d}{d h} (5 h x) - \frac{d}{d h} (3 h^{2} x) + \frac{d}{d h} (5 h^{2}) + \frac{d}{d h} (4 h^{3})

\frac{d}{d h} (7 h x^{2}) = 7 x^{2}

\frac{d}{d h} (5 h x) = 5 x

\frac{d}{d h} (3 h^{2} x) = 6 x h

\frac{d}{d h} (5 h^{2}) = 10 h

\frac{d}{d h} (4 h^{3}) = 12 h^{2}

= - 7 x^{2} - 5 x - 6 x h + 10 h + 12 h^{2}