derivative (3x)/(x^2-6)

Lösung

ableitung von

\frac{3 x}{x ^{2} - 6}

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int x sin (5 b x) d x

n = 1 \sum \infty \frac{x ^{n}}{5 ^{n}}

y^{^{'}} - \frac{2}{x} y = \frac{y ^{5}}{x ^{2}}, y (1) = 1

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

\frac{d}{d x} (cot (6 - x))