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Beliebt Rechnen >

derivative f(x)=(x+2)(2x^2-3)

Lösung

ableitung von

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

Lösung

6 x^{2} + 8 x - 3

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (2 x^{2} - 3) = 4 x

= 1 \cdot (2 x^{2} - 3) + 4 x (x + 2)

Vereinfache

1 \cdot (2 x^{2} - 3) + 4 x (x + 2) : 6 x^{2} + 8 x - 3

= 6 x^{2} + 8 x - 3

Graph

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a re a y = - x^{2} + 16, y = 0, x = - 2, x = 3

(dy)/(dx)=-(3x^2+2y^2)/(4xy)

\frac{d y}{d x} = - \frac{3 x ^{2} + 2 y ^{2}}{4 x y}