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Beliebt Rechnen >

derivative of (x-3(x^2+6))

Lösung

\frac{d}{d x} ((x - 3) (x^{2} + 6))

Lösung

3 x^{2} - 6 x + 6

Schritte zur Lösung

\frac{d}{d x} ((x - 3) (x^{2} + 6))

Wende die Produktregel an:

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

f = x - 3, g = x^{2} + 6

= \frac{d}{d x} (x - 3) (x^{2} + 6) + \frac{d}{d x} (x^{2} + 6) (x - 3)

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

\frac{d}{d x} (x^{2} + 6) = 2 x

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

Vereinfache

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

= 3 x^{2} - 6 x + 6

Graph

Beliebte Beispiele

steigung (17-13)(178)

s l o p e (17 - 13) (178)

(\partial)/(\partial x)(x/(cos(y)))

\frac{\partial}{\partial x} (\frac{x}{cos ( y )})

y^{^{'}} = x^{2} - 6 x + 14

\frac{d y}{d x} + 3 y = 4

y^{^{'}} = \frac{x + 1}{y}