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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{4}{x ^{7}} - e^{- 8 x})

\int \frac{x}{( x + 1 ) ( x + 2 )} d x

\frac{\partial}{\partial x} (1.015 E (m, x) b h^{3} m^{- 1} L^{- 4})

\frac{d}{d x} (cot^{4} (x) - csc^{4} (x))

d er i v a t i v e y = 2^{2 x}