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Beliebt Rechnen >

derivative of (3-x(2-x)(5-x))

Lösung

\frac{d}{d x} ((3 - x) (2 - x) (5 - x))

Lösung

- 3 x^{2} + 20 x - 31

Schritte zur Lösung

\frac{d}{d x} ((3 - x) (2 - x) (5 - x))

Wende die Produktregel an:

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

f = 3 - x, g = (2 - x) (5 - x)

= \frac{d}{d x} (3 - x) (2 - x) (5 - x) + \frac{d}{d x} ((2 - x) (5 - x)) (3 - x)

\frac{d}{d x} (3 - x) = - 1

\frac{d}{d x} ((2 - x) (5 - x)) = 2 x - 7

= (- 1) (2 - x) (5 - x) + (2 x - 7) (3 - x)

Vereinfache

(- 1) (2 - x) (5 - x) + (2 x - 7) (3 - x) : - 3 x^{2} + 20 x - 31

= - 3 x^{2} + 20 x - 31

Graph

Beliebte Beispiele

integral of (3x-2)e^x

\int (3 x - 2) e^{x} d x

integral of (x+3)^3

\int (x + 3)^{3} d x

integral of 2x(x^2+2)^2

\int 2 x (x^{2} + 2)^{2} d x

integral of 3cos^2(x)

\int 3 cos^{2} (x) d x

f(x)=xsin(x)+cos(x)

f (x) = x sin (x) + cos (x)