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Beliebt Rechnen >

derivative g(w)=9\sqrt[3]{w}

Lösung

ableitung von

g (w) = 9 3 w

Lösung

\frac{3}{w ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d w} (9 3 w)

Entferne die Konstante:

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

= 9 \frac{d}{d w} (3 w)

Wende Radikal Regel an:

n a = a^{\frac{1}{n}}

= 9 \frac{d}{d w} (w^{\frac{1}{3}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 9 \cdot \frac{1}{3} w^{\frac{1}{3} - 1}

Vereinfache

9 \cdot \frac{1}{3} w^{\frac{1}{3} - 1} : \frac{3}{w ^{\frac{2}{3}}}

= \frac{3}{w ^{\frac{2}{3}}}

Graph

Beliebte Beispiele

tangent y=sqrt(5x+20),\at x=1

t an g e n t y = 5 x + 20, at x = 1

derivative f(x)=16sqrt(x+3)

d er i v a t i v e f (x) = 16 x + 3

integral from-2 to 1 of x((4-x^2)-(x+2))

\int_{- 2}^{1} x ((4 - x^{2}) - (x + 2)) d x

dx=(e^{t^2}+2xt)dt

d x = (e^{t^{2}} + 2 x t) d t

integral of 13^x

\int 1 3^{x} d x