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

解答

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

2 a t (x - h)

求解步骤

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

将

a, k, t, h

视为常数

将常数提出:

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

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

使用微分加减法定则:

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

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

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

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

= t (2 a (x - h) + 0)

化简

= 2 a t (x - h)

e x p an d - \frac{48 s ^{3} - 114 s ^{2} + s + 1}{6 s ^{2} ( s ^{2} - 2 s + 5 )}

e x p an d \frac{6}{( 2 n - 1 ) ( 2 n + 1 )}

e x p an d - 3 (x + Δ x)^{2}

s im pl i f y (i + 3)^{5}

e x p an d \frac{sin ( θ )}{\frac{d}{d θ} ( ( θ x ( θ ) ) ( θ - sin ( θ ) ) )}