derivative (x^2-8x+5)/(x^2+8)

Lösung

ableitung von

\frac{x ^{2} - 8 x + 5}{x ^{2} + 8}

\frac{8 x ^{2} + 6 x - 64}{( x ^{2} + 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 8 x + 5}{x ^{2} + 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} - 8 x + 5 ) ( x ^{2} + 8 ) - \frac{d}{d x} ( x ^{2} + 8 ) ( x ^{2} - 8 x + 5 )}{( x ^{2} + 8 ) ^{2}}

\frac{d}{d x} (x^{2} - 8 x + 5) = 2 x - 8

\frac{d}{d x} (x^{2} + 8) = 2 x

= \frac{( 2 x - 8 ) ( x ^{2} + 8 ) - 2 x ( x ^{2} - 8 x + 5 )}{( x ^{2} + 8 ) ^{2}}

Multipliziere aus

(2 x - 8) (x^{2} + 8) - 2 x (x^{2} - 8 x + 5) : 8 x^{2} + 6 x - 64

= \frac{8 x ^{2} + 6 x - 64}{( x ^{2} + 8 ) ^{2}}

\int \frac{1}{4 x x ^{2} - 16} d x

\frac{d}{d x} (1 - cos (5 x))

x \to 1 lim (\frac{x + 3}{x + 1})

l a pl a ce t r an s f or m - 6 t^{2} δ (t - 5)

d er i v a t i v e 5 - 5 x^{3}