derivative of sqrt(3+\sqrt{7x)}

Lösung

\frac{d}{d x} (3 + 7 x)

\frac{7}{4 x 3 + 7 x}

Schritte zur Lösung

\frac{d}{d x} (3 + 7 x)

Wende die Kettenregel an:

\frac{1}{2 3 + 7 x} \frac{d}{d x} (3 + 7 x)

= \frac{1}{2 3 + 7 x} \frac{d}{d x} (3 + 7 x)

\frac{d}{d x} (3 + 7 x) = \frac{7}{2 x}

= \frac{1}{2 3 + 7 x} \cdot \frac{7}{2 x}

Vereinfache

\frac{1}{2 3 + 7 x} \cdot \frac{7}{2 x} : \frac{7}{4 x 3 + 7 x}

= \frac{7}{4 x 3 + 7 x}

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