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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Behandle

a, k, b, h

als Konstante

Wende die Summen-/Differenzregel an:

(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

Vereinfache

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

Graph

Beliebte Beispiele

d/(dt)(-60+20t)

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

derivative y=5x+x+5

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

derivative y=(e^x+sin(x))/2

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

derivative x^{1-x}

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

derivative (z-1)/(x^3)

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