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Beliebt Rechnen >

derivative of (x-a(x-b)(x-c))

Lösung

\frac{d}{d x} ((x - a) (x - b) (x - c))

Lösung

3 x^{2} - 2 a x - 2 b x - 2 c x + ab + b c + a c

Schritte zur Lösung

\frac{d}{d x} ((x - a) (x - b) (x - c))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x - a, g = (x - b) (x - c)

= \frac{d}{d x} (x - a) (x - b) (x - c) + \frac{d}{d x} ((x - b) (x - c)) (x - a)

\frac{d}{d x} (x - a) = 1

\frac{d}{d x} ((x - b) (x - c)) = 2 x - b - c

= 1 \cdot (x - b) (x - c) + (2 x - b - c) (x - a)

Vereinfache

1 \cdot (x - b) (x - c) + (2 x - b - c) (x - a) : 3 x^{2} - 2 a x - 2 b x - 2 c x + ab + b c + a c

= 3 x^{2} - 2 a x - 2 b x - 2 c x + ab + b c + a c

Graph

Beliebte Beispiele

(dy)/(dt)+(4y)/(200+3t)=8

\frac{d y}{d t} + \frac{4 y}{200 + 3 t} = 8

f(x)=2sec^2(x)tan(x)

f (x) = 2 sec^{2} (x) tan (x)

integral of (21)/((x^2-1)^2)

\int \frac{21}{( x ^{2} - 1 ) ^{2}} d x

d/(dt)(e^{-2t}{y}(t))

\frac{d}{d t} (e^{- 2 t} y (t))

derivative 2sin(2x)

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