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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{3 ( 2 x ^{2} + 1 ) ^{\frac{1}{2}}}{2} \cdot 4 x : 6 x (2 x^{2} + 1)^{\frac{1}{2}}

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

Graph

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