derivative of (x^2+3/(x^2-3))

Lösung

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3})

- \frac{12 x}{( x ^{2} - 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} + 3 ) ( x ^{2} - 3 ) - \frac{d}{d x} ( x ^{2} - 3 ) ( x ^{2} + 3 )}{( x ^{2} - 3 ) ^{2}}

\frac{d}{d x} (x^{2} + 3) = 2 x

\frac{d}{d x} (x^{2} - 3) = 2 x

= \frac{2 x ( x ^{2} - 3 ) - 2 x ( x ^{2} + 3 )}{( x ^{2} - 3 ) ^{2}}

Vereinfache

\frac{2 x ( x ^{2} - 3 ) - 2 x ( x ^{2} + 3 )}{( x ^{2} - 3 ) ^{2}} : - \frac{12 x}{( x ^{2} - 3 ) ^{2}}

= - \frac{12 x}{( x ^{2} - 3 ) ^{2}}

n = 1 \sum \infty \frac{n ^{2}}{5 ^{n}}

\int x^{2} - 4 d x

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

\frac{d}{d x} (\frac{3 - 4 x}{x ^{2} + 1})

x \to 1 - lim (2^{\frac{1}{x - 1}})