(\partial)/(\partial x)(1/(sqrt(2x)))

Lösung

\frac{\partial}{\partial x} (\frac{1}{2 x})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{2 x})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (2 x) = 2

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

Vereinfache

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

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

2 x y \frac{d y}{d x} = y^{2} - x^{2} + 1

t an g e n t 100 x^{2} + 400 x + 5000, 0.5

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