derivative of (x^2/(x-8))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{x - 8})

\frac{x ^{2} - 16 x}{( x - 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{x - 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( x - 8 ) - \frac{d}{d x} ( x - 8 ) x ^{2}}{( x - 8 ) ^{2}}

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

\frac{d}{d x} (x - 8) = 1

= \frac{2 x ( x - 8 ) - 1 \cdot x ^{2}}{( x - 8 ) ^{2}}

Vereinfache

\frac{2 x ( x - 8 ) - 1 \cdot x ^{2}}{( x - 8 ) ^{2}} : \frac{x ^{2} - 16 x}{( x - 8 ) ^{2}}

= \frac{x ^{2} - 16 x}{( x - 8 ) ^{2}}

\int \frac{x ^{2}}{x ^{2} + x + 6} d x

t an g e n t x + \frac{1}{x ^{3}}

x \to 2 lim (x^{2} - 4)

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

x \to 1 lim (x - 5)