derivative of (6(x^2+1)/((x^2-3)^3))

Lösung

\frac{d}{d x} (\frac{6 ( x ^{2} + 1 )}{( x ^{2} - 3 ) ^{3}})

- \frac{24 x ( x ^{2} + 3 )}{( x ^{2} - 3 ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{6 ( x ^{2} + 1 )}{( x ^{2} - 3 ) ^{3}})

Entferne die Konstante:

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

= 6 \frac{d}{d x} (\frac{x ^{2} + 1}{( x ^{2} - 3 ) ^{3}})

Wende die Quotientenregel an:

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

= 6 \cdot \frac{\frac{d}{d x} ( x ^{2} + 1 ) ( x ^{2} - 3 ) ^{3} - \frac{d}{d x} ( ( x ^{2} - 3 ) ^{3} ) ( x ^{2} + 1 )}{( ( x ^{2} - 3 ) ^{3} ) ^{2}}

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

\frac{d}{d x} ((x^{2} - 3)^{3}) = 6 x (x^{2} - 3)^{2}

= 6 \cdot \frac{2 x ( x ^{2} - 3 ) ^{3} - 6 x ( x ^{2} - 3 ) ^{2} ( x ^{2} + 1 )}{( ( x ^{2} - 3 ) ^{3} ) ^{2}}

Vereinfache

6 \cdot \frac{2 x ( x ^{2} - 3 ) ^{3} - 6 x ( x ^{2} - 3 ) ^{2} ( x ^{2} + 1 )}{( ( x ^{2} - 3 ) ^{3} ) ^{2}} : - \frac{24 x ( x ^{2} + 3 )}{( x ^{2} - 3 ) ^{4}}

= - \frac{24 x ( x ^{2} + 3 )}{( x ^{2} - 3 ) ^{4}}

a re a e^{x}, x e^{x^{2}}, 0, 1

in v erse l a pl a ce \frac{2 s + 5}{s ^{2} + 6 s + 34}

(y + x^{2} + y^{2}) d x = x d y

\int \frac{6 x ^{2}}{( x ^{6} + 1 ) ( x ^{3} + 1 )} d x

x \to 0 lim (sin (9 x))