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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 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} x^{- \frac{1}{2} - 1})

Vereinfache

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

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

\int \frac{1}{4 e ^{- 8 x} + e ^{8 x}} d x

\frac{\partial}{\partial x} (x (x^{2} + y^{2} + z^{2} - 1))

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

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

\int \frac{2 x + 1}{x ^{2} + x - 2} d x