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Beliebt Rechnen >

derivative of-2(x+3(x-3)^2)

Lösung

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

Lösung

- 2 (3 x^{2} - 6 x - 9)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x + 3, g = (x - 3)^{2}

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

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

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

= - 2 (1 \cdot (x - 3)^{2} + 2 (x - 3) (x + 3))

Vereinfache

- 2 (1 \cdot (x - 3)^{2} + 2 (x - 3) (x + 3)) : - 2 (3 x^{2} - 6 x - 9)

= - 2 (3 x^{2} - 6 x - 9)

Graph

Beliebte Beispiele

derivative of (cos(y+2e^{-x}cos(x))/y)

\frac{d}{d x} (\frac{cos ( y ) + 2 e ^{- x} cos ( x )}{y})

tangent y=3xe^x,(0,0)

t an g e n t y = 3 x e^{x}, (0, 0)

y^{^{'}} = x y + x

\frac{d y}{d t} + 6 y = 0

integral from-1 to 1 of (2-2x^2)^2

\int_{- 1}^{1} (2 - 2 x^{2})^{2} d x