(\partial)/(\partial x)((x^2+y^2)/(2x))

Lösung

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

\frac{x ^{2} - y ^{2}}{2 x ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{\partial}{\partial x} (x^{2} + y^{2}) = 2 x

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

= \frac{1}{2} \cdot \frac{2 xx - 1 \cdot ( x ^{2} + y ^{2} )}{x ^{2}}

Vereinfache

\frac{1}{2} \cdot \frac{2 xx - 1 \cdot ( x ^{2} + y ^{2} )}{x ^{2}} : \frac{x ^{2} - y ^{2}}{2 x ^{2}}

= \frac{x ^{2} - y ^{2}}{2 x ^{2}}

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

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