derivative of-(10x/((x^2-4)^2))

Lösung

\frac{d}{d x} (- \frac{10 x}{( x ^{2} - 4 ) ^{2}})

- \frac{10 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (- \frac{10 x}{( x ^{2} - 4 ) ^{2}})

Entferne die Konstante:

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

= - 10 \frac{d}{d x} (\frac{x}{( x ^{2} - 4 ) ^{2}})

Wende die Quotientenregel an:

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

= - 10 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 4 ) ^{2} - \frac{d}{d x} ( ( x ^{2} - 4 ) ^{2} ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}}

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

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

= - 10 \cdot \frac{1 \cdot ( x ^{2} - 4 ) ^{2} - 4 x ( x ^{2} - 4 ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}}

Vereinfache

- 10 \cdot \frac{1 \cdot ( x ^{2} - 4 ) ^{2} - 4 x ( x ^{2} - 4 ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}} : - \frac{10 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

= - \frac{10 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

t an g e n t f (x) = \frac{1}{x + 8}, at x = 9

n = 2 \sum \infty \frac{1}{n ^{3}}

\int \frac{x}{5 + 4 x - x ^{2}} d x

\int_{1}^{\infty} x^{2} d x

d er i v a t i v e f (x) = \frac{2 x ^{2} + 6 x + 6}{x + 1}