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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

= 6 \cdot \frac{1 \cdot ( x ^{2} - 1 ) ^{2} - 4 x ( x ^{2} - 1 ) x}{( ( x ^{2} - 1 ) ^{2} ) ^{2}}

Vereinfache

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

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

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

\int_{4}^{9} x d x

f (x) = sin (x) + x cos (x)

d er i v a t i v e f (x) = x + 3

t y^{^{'}} + 4 y = t^{2} - t + 1