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

Lösung

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

\frac{25}{( x ^{2} + 5 ) x ^{2} + 5}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

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

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

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

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

Vereinfache

5 \cdot \frac{1 \cdot x ^{2} + 5 - \frac{x}{x ^{2} + 5} x}{( x ^{2} + 5 ) ^{2}} : \frac{25}{( x ^{2} + 5 ) x ^{2} + 5}

= \frac{25}{( x ^{2} + 5 ) x ^{2} + 5}

\int_{0}^{\frac{π}{2}} sin^{2} (2 x) d x

\int (3 x - 6) d x

x \to 5 - lim (\frac{2}{( x - 5 ) ^{3}})

\frac{d}{d x} (\frac{sin ( x )}{3 x ^{2}})

x \to 3 lim (g (x))