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

Lösung

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

- \frac{1}{4 x ^{\frac{3}{2}}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= \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}

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

Vereinfache

\frac{1}{2} (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : - \frac{1}{4 x ^{\frac{3}{2}}}

= - \frac{1}{4 x ^{\frac{3}{2}}}

\int \frac{x ^{5}}{x ^{6} + 5} d x

l a pl a ce t r an s f or m (e^{4 t} - e^{- 3 t})^{2}

\frac{d}{d x} ((x^{2} - 4)^{5} (3 x + 5)^{4})

\int \frac{5 x - 3}{( x + 1 ) ( x - 3 )} d x

(y^{2} - 2 x y + 6 x) d x - (x^{2} - 2 x y + 2) d y = 0