derivative of x/(sqrt(x^2+64))

Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 64})

\frac{64}{( x ^{2} + 64 ) x ^{2} + 64}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 64})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} x ^{2} + 64 - \frac{d}{d x} ( x ^{2} + 64 ) x}{( x ^{2} + 64 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} + 64) = \frac{x}{x ^{2} + 64}

= \frac{1 \cdot x ^{2} + 64 - \frac{x}{x ^{2} + 64} x}{( x ^{2} + 64 ) ^{2}}

Vereinfache

\frac{1 \cdot x ^{2} + 64 - \frac{x}{x ^{2} + 64} x}{( x ^{2} + 64 ) ^{2}} : \frac{64}{( x ^{2} + 64 ) x ^{2} + 64}

= \frac{64}{( x ^{2} + 64 ) x ^{2} + 64}

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