derivative of (x^2-4/(x^2-3))

Lösung

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

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

Schritte zur Lösung

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

\frac{d}{d x} (x^{2} - 4) = 2 x

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

= \frac{2 x ( x ^{2} - 3 ) - 2 x ( x ^{2} - 4 )}{( x ^{2} - 3 ) ^{2}}

Multipliziere aus

2 x (x^{2} - 3) - 2 x (x^{2} - 4) : 2 x

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

i = 0 \sum \infty (\frac{1}{3})^{i}

\frac{\partial}{\partial x} (\frac{1}{1 + x ^{2} + y ^{2}})

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

x \to 2 lim (x^{2} + 3 x - 1)

\frac{\partial}{\partial x} (\frac{4 x - 6 y}{y ^{2} + 2 x ^{2}})