derivative of \sqrt[3]{x^2+3}

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d y}{d x} = 9.8 - 0.2 y

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