derivative of 3/(x(x^2-4))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

s l o p e x y - 2 y^{2} = 3

\frac{\partial}{\partial x} (6 y^{\frac{x}{z}})

sec (x) d y = x cot (y) d x

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

v o l u m e ab o u t y = 0, y = x, [0, 1]