derivative (10x)/(x^2-6)

Lösung

ableitung von

\frac{10 x}{x ^{2} - 6}

\frac{10 ( - x ^{2} - 6 )}{( x ^{2} - 6 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{10 x}{x ^{2} - 6})

Entferne die Konstante:

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

= 10 \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}}

= 10 \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

= 10 \cdot \frac{1 \cdot ( x ^{2} - 6 ) - 2 xx}{( x ^{2} - 6 ) ^{2}}

Vereinfache

10 \cdot \frac{1 \cdot ( x ^{2} - 6 ) - 2 xx}{( x ^{2} - 6 ) ^{2}} : \frac{10 ( - x ^{2} - 6 )}{( x ^{2} - 6 ) ^{2}}

= \frac{10 ( - x ^{2} - 6 )}{( x ^{2} - 6 ) ^{2}}

\frac{d}{d x} (n x)

\frac{d}{d x} ((x^{2} + 1)^{0.6})

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

\frac{d}{d t} (- 8 cos (t))

\frac{d}{d x} (ln (\frac{x + a}{y}))