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Beliebt Rechnen >

derivative (x^3+7)^{2/3}

Lösung

ableitung von

(x^{3} + 7)^{\frac{2}{3}}

Lösung

\frac{2 x ^{2}}{( x ^{3} + 7 ) ^{\frac{1}{3}}}

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + 7)^{\frac{2}{3}})

Wende die Kettenregel an:

\frac{2}{3 ( x ^{3} + 7 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{3} + 7)

= \frac{2}{3 ( x ^{3} + 7 ) ^{\frac{1}{3}}} \frac{d}{d x} (x^{3} + 7)

\frac{d}{d x} (x^{3} + 7) = 3 x^{2}

= \frac{2}{3 ( x ^{3} + 7 ) ^{\frac{1}{3}}} \cdot 3 x^{2}

Vereinfache

\frac{2}{3 ( x ^{3} + 7 ) ^{\frac{1}{3}}} \cdot 3 x^{2} : \frac{2 x ^{2}}{( x ^{3} + 7 ) ^{\frac{1}{3}}}

= \frac{2 x ^{2}}{( x ^{3} + 7 ) ^{\frac{1}{3}}}

Graph

Beliebte Beispiele

tangent f(x)=-3x^2-3x+2,\at x=1

t an g e n t f (x) = - 3 x^{2} - 3 x + 2, at x = 1

derivative f(x)=3x^2+e^{2x}+pi^2

d er i v a t i v e f (x) = 3 x^{2} + e^{2 x} + π^{2}

derivative of (x^2/((x-2)^2))

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

derivative 7x\sqrt[3]{x}

d er i v a t i v e 7 x 3 x

integral of x(x^3+1)

\int x (x^{3} + 1) d x