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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (3) = 0

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

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

= \frac{1}{6} (0 + 2 - 3 x^{2})

Vereinfache

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

Graph

Beliebte Beispiele

y^{^{'}} = t \cdot y

integral of 6sin(x)

\int 6 sin (x) d x

tangent f(x)=x^2-6x,\at x=7

t an g e n t f (x) = x^{2} - 6 x, at x = 7

integral of-2x+1

\int - 2 x + 1 d x

derivative f(x)=(-8x+2)/(3x+5)

d er i v a t i v e f (x) = \frac{- 8 x + 2}{3 x + 5}