derivative of (x^2+3/(x^2-1))

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

Vereinfache

\frac{2 x ( x ^{2} - 1 ) - 2 x ( x ^{2} + 3 )}{( x ^{2} - 1 ) ^{2}} : - \frac{8 x}{( x ^{2} - 1 ) ^{2}}

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

d er i v a t i v e \frac{sin ( 4 t )}{cos ( 6 t )}

d er i v a t i v e y = x^{3 x}

y^{^{''}} + y = sec (t)

n = 1 \sum \infty \frac{6 n}{9 - 2 n}

ma c l a u r in f (x) = (1 + x)^{- \frac{5}{3}}