derivative of (x^2/(x^2-6))

Lösung

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

- \frac{12 x}{( x ^{2} - 6 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 x ( x ^{2} - 6 ) - 2 x x ^{2}}{( x ^{2} - 6 ) ^{2}} : - \frac{12 x}{( x ^{2} - 6 ) ^{2}}

= - \frac{12 x}{( x ^{2} - 6 ) ^{2}}

a re a 6 - x^{2}, x^{2} - 20 < x < 3

d er i v a t i v e 4 x - 20

x \to \infty lim (x^{4} e^{x})

t a y l or ln (5 - x)

y^{^{''}} + 484 y = sec (22 x)