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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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