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Beliebt Rechnen >

(\partial)/(\partial x)(3(((4+x))/(5+z))^2)

Lösung

\frac{\partial}{\partial x} (3 (\frac{( 4 + x )}{5 + z})^{2})

Lösung

\frac{6 ( 4 + x )}{( 5 + z ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (3 (\frac{( 4 + x )}{5 + z})^{2})

Behandle

z

als Konstante

Entferne die Konstante:

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

= 3 \frac{\partial}{\partial x} ((\frac{4 + x}{5 + z})^{2})

Wende die Kettenregel an:

2 \cdot \frac{4 + x}{5 + z} \frac{\partial}{\partial x} (\frac{4 + x}{5 + z})

= 2 \cdot \frac{4 + x}{5 + z} \frac{\partial}{\partial x} (\frac{4 + x}{5 + z})

\frac{\partial}{\partial x} (\frac{4 + x}{5 + z}) = \frac{1}{5 + z}

= 3 \cdot 2 \cdot \frac{4 + x}{5 + z} \cdot \frac{1}{5 + z}

Vereinfache

3 \cdot 2 \cdot \frac{4 + x}{5 + z} \cdot \frac{1}{5 + z} : \frac{6 ( 4 + x )}{( 5 + z ) ^{2}}

= \frac{6 ( 4 + x )}{( 5 + z ) ^{2}}

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