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

解答

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

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

求解步骤

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

化简

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

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

将

a, k, b, h

视为常数

使用微分加减法定则:

(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

化简

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

\frac{d}{d t} (- 60 + 20 t)

d er i v a t i v e y = 5 x + x + 5

d er i v a t i v e y = \frac{e ^{x} + sin ( x )}{2}

d er i v a t i v e x^{1 - x}

d er i v a t i v e \frac{z - 1}{x ^{3}}