(\partial)/(\partial x)(pi(x/2)^2h)

Lösung

\frac{\partial}{\partial x} (π (\frac{x}{2})^{2} h)

\frac{πh x}{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (π (\frac{x}{2})^{2} h)

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

= πh \cdot 2 \cdot \frac{x}{2} \cdot \frac{1}{2}

Vereinfache

πh \cdot 2 \cdot \frac{x}{2} \cdot \frac{1}{2} : \frac{πh x}{2}

= \frac{πh x}{2}

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