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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int 4 x^{2} + 9 d x

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

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

x \to 0 lim (tan (2 x))

\frac{d}{d x} (3 x + 9)