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

Lösung

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

\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}}}

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