derivative of x/(sqrt(x^2+6))

Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 6})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 6})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} x ^{2} + 6 - \frac{d}{d x} ( x ^{2} + 6 ) x}{( x ^{2} + 6 ) ^{2}}

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

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

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

Vereinfache

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

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

\int (1 - x) (e^{- x} + 1) d x

\frac{d ^{2} y}{d x ^{2}} + \frac{4}{5} \frac{d y}{d x} + \frac{8}{5} y = 0

t \to 1 lim (\frac{5 t - 1}{t + 1})

\frac{\partial}{\partial x} (\frac{a}{s} cos^{2} (x))

n = 1 \sum \infty \frac{n - 6}{n + 6}