derivative x/(x^2-7)

Lösung

ableitung von

\frac{x}{x ^{2} - 7}

\frac{- x ^{2} - 7}{( x ^{2} - 7 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} - 7})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x ^{2} - 7 ) - \frac{d}{d x} ( x ^{2} - 7 ) x}{( x ^{2} - 7 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 7) = 2 x

= \frac{1 \cdot ( x ^{2} - 7 ) - 2 xx}{( x ^{2} - 7 ) ^{2}}

1 \cdot (x^{2} - 7) - 2 xx = - x^{2} - 7

= \frac{- x ^{2} - 7}{( x ^{2} - 7 ) ^{2}}

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

\int 3 + 2 x y d x

d er i v a t i v e y = - 2 x - 4

\frac{d}{d x} (\frac{A x + B}{4 - x})

n = 1 \sum \infty \frac{3}{n !}