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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= 6 (4 x + 1)^{\frac{1}{2}}

Graph

Beliebte Beispiele

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