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Beliebt Rechnen >

derivative of (x-1^2(x-2)(x-4))

Lösung

\frac{d}{d x} ((x - 1)^{2} (x - 2) (x - 4))

Lösung

4 x^{3} - 24 x^{2} + 42 x - 22

Schritte zur Lösung

\frac{d}{d x} ((x - 1)^{2} (x - 2) (x - 4))

Wende die Produktregel an:

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

f = (x - 1)^{2}, g = (x - 2) (x - 4)

= \frac{d}{d x} ((x - 1)^{2}) (x - 2) (x - 4) + \frac{d}{d x} ((x - 2) (x - 4)) (x - 1)^{2}

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

\frac{d}{d x} ((x - 2) (x - 4)) = 2 x - 6

= 2 (x - 1) (x - 2) (x - 4) + (2 x - 6) (x - 1)^{2}

Vereinfache

2 (x - 1) (x - 2) (x - 4) + (2 x - 6) (x - 1)^{2} : 4 x^{3} - 24 x^{2} + 42 x - 22

= 4 x^{3} - 24 x^{2} + 42 x - 22

Graph

Beliebte Beispiele

tangent y=(2x)/((x^2+1))

t an g e n t y = \frac{2 x}{( x ^{2} + 1 )}

integral of (6-72x)/(sqrt(1-36x^2))

\int \frac{6 - 72 x}{1 - 36 x ^{2}} d x

derivative of (sqrt(x)/(x+2))

\frac{d}{d x} (\frac{x}{x + 2})

derivative of (x+4/(x-5))

\frac{d}{d x} (\frac{x + 4}{x - 5})

derivative sqrt(23x)

d er i v a t i v e 23 x