derivative (x^2+4)/(x^2-4)

Lösung

ableitung von

\frac{x ^{2} + 4}{x ^{2} - 4}

- \frac{16 x}{( x ^{2} - 4 ) ^{2}}

Schritte zur Lösung

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

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

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

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

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

Vereinfache

\frac{2 x ( x ^{2} - 4 ) - 2 x ( x ^{2} + 4 )}{( x ^{2} - 4 ) ^{2}} : - \frac{16 x}{( x ^{2} - 4 ) ^{2}}

= - \frac{16 x}{( x ^{2} - 4 ) ^{2}}

a re a 6 - 6 x^{2}, 0

\frac{d}{d x} (- \frac{3}{8 x ^{\frac{5}{2}}})

\int sec^{2} (5 x) + e^{\frac{x}{2}} d x

\int \frac{x ^{2} + 1}{x ^{2} + x - 2} d x

y^{^{'}} (t) = (y + 1) (y - 3), y (0) = 1