derivative (x^2-9x+1)/(x^2+5)

Lösung

ableitung von

\frac{x ^{2} - 9 x + 1}{x ^{2} + 5}

\frac{9 x ^{2} + 8 x - 45}{( x ^{2} + 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 9 x + 1}{x ^{2} + 5})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} - 9 x + 1 ) ( x ^{2} + 5 ) - \frac{d}{d x} ( x ^{2} + 5 ) ( x ^{2} - 9 x + 1 )}{( x ^{2} + 5 ) ^{2}}

\frac{d}{d x} (x^{2} - 9 x + 1) = 2 x - 9

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

= \frac{( 2 x - 9 ) ( x ^{2} + 5 ) - 2 x ( x ^{2} - 9 x + 1 )}{( x ^{2} + 5 ) ^{2}}

Multipliziere aus

(2 x - 9) (x^{2} + 5) - 2 x (x^{2} - 9 x + 1) : 9 x^{2} + 8 x - 45

= \frac{9 x ^{2} + 8 x - 45}{( x ^{2} + 5 ) ^{2}}

d er i v a t i v e 5 sin^{2} (t)

\frac{d}{d x} (4 x sin (x^{2}))

\frac{d}{d x} (\frac{2 - x}{1 - y})

\int \frac{1}{4} sin (4 x) d x

s l o p e (- 3, 3), (4, - 5)