(\partial)/(\partial w)(1/(2sqrt(v-w)))

Lösung

\frac{\partial}{\partial w} (\frac{1}{2 v - w})

\frac{1}{4 ( v - w ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{\partial}{\partial w} (\frac{1}{2 v - w})

Behandle

v

als Konstante

Entferne die Konstante:

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

= \frac{1}{2} \frac{\partial}{\partial w} (\frac{1}{v - w})

Wende Exponentenregel an:

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

= \frac{1}{2} \frac{\partial}{\partial w} ((v - w)^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( v - w ) ^{\frac{3}{2}}} \frac{\partial}{\partial w} (v - w)

= - \frac{1}{2 ( v - w ) ^{\frac{3}{2}}} \frac{\partial}{\partial w} (v - w)

\frac{\partial}{\partial w} (v - w) = - 1

= \frac{1}{2} (- \frac{1}{2 ( v - w ) ^{\frac{3}{2}}} (- 1))

Vereinfache

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

= \frac{1}{4 ( v - w ) ^{\frac{3}{2}}}

\int cosh^{3} (x) d x

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