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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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