derivative of (5x/(sqrt(x^2+1)))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

= 5 \cdot \frac{1 \cdot x ^{2} + 1 - \frac{x}{x ^{2} + 1} x}{( x ^{2} + 1 ) ^{2}}

Vereinfache

5 \cdot \frac{1 \cdot x ^{2} + 1 - \frac{x}{x ^{2} + 1} x}{( x ^{2} + 1 ) ^{2}} : \frac{5}{( x ^{2} + 1 ) x ^{2} + 1}

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

\frac{d}{d x} ((3 x - 4)^{2})

\frac{d}{d x} (x (12 - 2 x)^{2})

\int 8 e^{4 x} cos (6 x) d x

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