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

Lösung

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

\frac{12 x}{( x ^{2} + 2 ) ^{2}}

Schritte zur Lösung

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

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

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

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

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

Multipliziere aus

2 x (x^{2} + 2) - 2 x (x^{2} - 4) : 12 x

= \frac{12 x}{( x ^{2} + 2 ) ^{2}}

t an g e n t e^{x} (5 - 4 x + 4 x^{2})

\frac{\partial}{\partial x} (x^{3} e^{- 2 y})

y = (7 x + 4) x^{2}

\frac{d}{d t} (s - t)

y^{^{''}} - 2 y^{^{'}} = 8 sin (2 x) + 2 x e^{2 x}