derivative of (x^2-4/(x^2+1))

Lösung

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

\frac{10 x}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

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

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

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

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

Multipliziere aus

2 x (x^{2} + 1) - 2 x (x^{2} - 4) : 10 x

= \frac{10 x}{( x ^{2} + 1 ) ^{2}}

d er i v a t i v e y = 220 + 65 x

d er i v a t i v e f (x) = \frac{x}{x + 8}

(15 x y^{2} - 4 y) + (15 x^{2} y - 4 x) y^{^{'}} = 0

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

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