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

Lösung

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

\frac{24 x ( x ^{2} + 1 )}{( 1 - x ^{2} ) ^{4}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{24 x ( x ^{2} + 1 )}{( 1 - x ^{2} ) ^{4}}

\int_{- a}^{a} \int_{0}^{1} sin (y) e^{x^{2}} d x d y

f (x) = x 1 - x^{2}

\int_{1}^{8} \frac{1}{3 x + 1} d x

x \to - 1 lim (\frac{1}{x + 1})

y^{^{''}} - y^{^{'}} + 4 y = 2 sin (2 t)