(\partial)/(\partial x)((6x)/(sqrt(x^2+5)))

Lösung

\frac{\partial}{\partial x} (\frac{6 x}{x ^{2} + 5})

\frac{30}{( x ^{2} + 5 ) x ^{2} + 5}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{6 x}{x ^{2} + 5})

Entferne die Konstante:

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

= 6 \frac{\partial}{\partial x} (\frac{x}{x ^{2} + 5})

Wende die Quotientenregel an:

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

= 6 \cdot \frac{\frac{\partial}{\partial x} ( x ) x ^{2} + 5 - \frac{\partial}{\partial x} ( x ^{2} + 5 ) x}{( x ^{2} + 5 ) ^{2}}

\frac{\partial}{\partial x} (x) = 1

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

= 6 \cdot \frac{1 \cdot x ^{2} + 5 - \frac{x}{x ^{2} + 5} x}{( x ^{2} + 5 ) ^{2}}

Vereinfache

6 \cdot \frac{1 \cdot x ^{2} + 5 - \frac{x}{x ^{2} + 5} x}{( x ^{2} + 5 ) ^{2}} : \frac{30}{( x ^{2} + 5 ) x ^{2} + 5}

= \frac{30}{( x ^{2} + 5 ) x ^{2} + 5}

\int 4 ln (x) d x

\frac{\partial}{\partial x} (x^{7} y^{8} + 3 x^{5} y)

n = 0 \sum \infty \frac{2 n}{n + 3}

x \frac{d y}{d x} + y = - 5 x y^{2}

\int x^{4} - \frac{2}{x} d x