(\partial)/(\partial x)(2sqrt(x^2+12^2))

Lösung

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

\frac{2 x}{x ^{2} + 144}

Schritte zur Lösung

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

Vereinfache

2 x^{2} + 1 2^{2} : 2 x^{2} + 144

= \frac{\partial}{\partial x} (2 x^{2} + 144)

Entferne die Konstante:

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

= 2 \frac{\partial}{\partial x} (x^{2} + 144)

Wende die Kettenregel an:

\frac{1}{2 x ^{2} + 144} \frac{\partial}{\partial x} (x^{2} + 144)

= \frac{1}{2 x ^{2} + 144} \frac{\partial}{\partial x} (x^{2} + 144)

\frac{\partial}{\partial x} (x^{2} + 144) = 2 x

= 2 \cdot \frac{1}{2 x ^{2} + 144} \cdot 2 x

Vereinfache

2 \cdot \frac{1}{2 x ^{2} + 144} \cdot 2 x : \frac{2 x}{x ^{2} + 144}

= \frac{2 x}{x ^{2} + 144}

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