derivative of x/(sqrt(x^2-9))

Lösung

\frac{d}{d x} (\frac{x}{x ^{2} - 9})

- \frac{9}{( x ^{2} - 9 ) x ^{2} - 9}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} - 9})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} x ^{2} - 9 - \frac{d}{d x} ( x ^{2} - 9 ) x}{( x ^{2} - 9 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 9) = \frac{x}{x ^{2} - 9}

= \frac{1 \cdot x ^{2} - 9 - \frac{x}{x ^{2} - 9} x}{( x ^{2} - 9 ) ^{2}}

Vereinfache

\frac{1 \cdot x ^{2} - 9 - \frac{x}{x ^{2} - 9} x}{( x ^{2} - 9 ) ^{2}} : - \frac{9}{( x ^{2} - 9 ) x ^{2} - 9}

= - \frac{9}{( x ^{2} - 9 ) x ^{2} - 9}

\int \frac{1}{64 e ^{- 7 x} + e ^{7 x}} d x

x \to 0 lim (\frac{5}{x + x ^{2}})

d er i v a t i v e f (x) = 10 x + 6

d er i v a t i v e \frac{x ^{2} - 2 x}{x + 1}

d er i v a t i v e y = - x