derivative f(x)= x/(x^2-7)

Lösung

ableitung von

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

n \to 2 lim (\frac{1}{n ^{2}})

x \to 2 + lim (x^{2} - 4)

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

\frac{d}{d x} (6 x^{2} + 5 x)