derivative (3x)^{1/2}

Lösung

ableitung von

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

\frac{3 ^{\frac{1}{2}}}{2 x ^{\frac{1}{2}}}

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 3^{\frac{1}{2}} \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Vereinfache

3^{\frac{1}{2}} \cdot \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{3 ^{\frac{1}{2}}}{2 x ^{\frac{1}{2}}}

= \frac{3 ^{\frac{1}{2}}}{2 x ^{\frac{1}{2}}}

d er i v a t i v e y = ln (x) sec^{3} (x)

\frac{d}{d t} (15 + 300 t)

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d er i v a t i v e \frac{y}{( x - y ) 2}

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