derivative (x(x^2+4))^{1/3}

Lösung

ableitung von

(x (x^{2} + 4))^{\frac{1}{3}}

\frac{3 x ^{2} + 4}{3 ( x ( x ^{2} + 4 ) ) ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} ((x (x^{2} + 4))^{\frac{1}{3}})

Wende die Kettenregel an:

\frac{1}{3 ( x ( x ^{2} + 4 ) ) ^{\frac{2}{3}}} \frac{d}{d x} (x (x^{2} + 4))

= \frac{1}{3 ( x ( x ^{2} + 4 ) ) ^{\frac{2}{3}}} \frac{d}{d x} (x (x^{2} + 4))

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

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

Vereinfache

\frac{1}{3 ( x ( x ^{2} + 4 ) ) ^{\frac{2}{3}}} (3 x^{2} + 4) : \frac{3 x ^{2} + 4}{3 ( x ( x ^{2} + 4 ) ) ^{\frac{2}{3}}}

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

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

\int 4 x^{2} + \frac{1}{( 2 x ) ^{2}} d x

l a pl a ce t r an s f or m 2 t^{4}

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\frac{d y}{d x} = x - 2.5 y