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

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

= 2^{\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}

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

Vereinfache

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

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

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

x \to - 2 lim (- x^{2} + 5 x - 1)

in v erse l a pl a ce F (s) = \frac{s ^{2} - 2 s - 6}{s - 2}

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

\frac{d}{d x} (x^{l n (x)})