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

Lösung

\frac{d}{d x} ((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}}}

\frac{d}{d x} (14 e^{2 x})

(cos (6 x)) y^{^{'}} - 6 (tan (6 x)) y = - 2 sec (6 x)

\frac{d}{d x} ((x^{6} - 6) x)

d er i v a t i v e x sin (x)

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