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

Lösung

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

\frac{- x ^{4} - 3 x ^{2} - 2 x}{( x ^{3} - 1 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Multipliziere aus

2 x (x^{3} - 1) - 3 x^{2} (x^{2} + 1) : - x^{4} - 3 x^{2} - 2 x

= \frac{- x ^{4} - 3 x ^{2} - 2 x}{( x ^{3} - 1 ) ^{2}}

d er i v a t i v e f (x) = 17 e^{e} - e x^{e}

l a pl a ce t r an s f or m e^{- t} t sin (2 t)

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

x \to \infty lim ((e)^{x})

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