derivative of a(b(x-h)^2+k)

解

\frac{d}{d x} (a (b (x - h))^{2} + k)

2 a b^{2} (x - h)

解答ステップ

\frac{d}{d x} (a (b (x - h))^{2} + k)

簡素化

a (b (x - h))^{2} + k : a b^{2} (x - h)^{2} + k

= \frac{d}{d x} (a b^{2} (x - h)^{2} + k)

a, k, b, h

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 x} (a b^{2} (x - h)^{2}) + \frac{d k}{d x}

\frac{d}{d x} (a b^{2} (x - h)^{2}) = 2 a b^{2} (x - h)

\frac{d k}{d x} = 0

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

簡素化

= 2 a b^{2} (x - h)