derivative of 8sqrt(7x^2+5)

Lösung

\frac{d}{d x} (8 7 x^{2} + 5)

\frac{56 x}{7 x ^{2} + 5}

Schritte zur Lösung

\frac{d}{d x} (8 7 x^{2} + 5)

Entferne die Konstante:

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

= 8 \frac{d}{d x} (7 x^{2} + 5)

Wende die Kettenregel an:

\frac{1}{2 7 x ^{2} + 5} \frac{d}{d x} (7 x^{2} + 5)

= \frac{1}{2 7 x ^{2} + 5} \frac{d}{d x} (7 x^{2} + 5)

\frac{d}{d x} (7 x^{2} + 5) = 14 x

= 8 \cdot \frac{1}{2 7 x ^{2} + 5} \cdot 14 x

Vereinfache

8 \cdot \frac{1}{2 7 x ^{2} + 5} \cdot 14 x : \frac{56 x}{7 x ^{2} + 5}

= \frac{56 x}{7 x ^{2} + 5}

\frac{d}{d x} (\frac{x}{x - 10})

\frac{d y}{d x} = \frac{2 x - 3}{5 y}

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

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