derivative of (4x/((1-x^2)^2))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

= 4 \cdot \frac{\frac{d x}{d x} ( 1 - x ^{2} ) ^{2} - \frac{d}{d x} ( ( 1 - x ^{2} ) ^{2} ) x}{( ( 1 - x ^{2} ) ^{2} ) ^{2}}

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

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

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

Vereinfache

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

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

t an g e n t f (x) = x^{2} + 3 x + 2, at x = 1

l a pl a ce t r an s f or m e^{- 2 t} cos (2 t)

d er i v a t i v e f (x) = 7 x^{3}

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

\int sin^{2} (6 x) cos^{2} (6 x) d x