derivative of x/(x^3+1)

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

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

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

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

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

d er i v a t i v e f (x) = cos^{2} (2 x)

d er i v a t i v e \frac{1 - 2 x}{1 + 2 x}

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

\frac{d}{d x} (e^{x^{2}} y)

\int \frac{1}{3} x^{2} d x