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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (e^{x y^{2}} 2 x y)

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