derivative (x^2-5x+3)/(x^2+7)

Lösung

ableitung von

\frac{x ^{2} - 5 x + 3}{x ^{2} + 7}

\frac{5 x ^{2} + 8 x - 35}{( x ^{2} + 7 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 5 x + 3}{x ^{2} + 7})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} - 5 x + 3 ) ( x ^{2} + 7 ) - \frac{d}{d x} ( x ^{2} + 7 ) ( x ^{2} - 5 x + 3 )}{( x ^{2} + 7 ) ^{2}}

\frac{d}{d x} (x^{2} - 5 x + 3) = 2 x - 5

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

= \frac{( 2 x - 5 ) ( x ^{2} + 7 ) - 2 x ( x ^{2} - 5 x + 3 )}{( x ^{2} + 7 ) ^{2}}

Multipliziere aus

(2 x - 5) (x^{2} + 7) - 2 x (x^{2} - 5 x + 3) : 5 x^{2} + 8 x - 35

= \frac{5 x ^{2} + 8 x - 35}{( x ^{2} + 7 ) ^{2}}

t an g e n t f (x) = - 5 x^{2} + 2 x

d er i v a t i v e f (x) = 5 x^{2} + 3

\frac{d}{d x} (\frac{3 sin ( x ) - 11 cos ( x )}{x - 2})

n = 1 \sum \infty \frac{n ^{n}}{5 ^{n}}

\int \frac{1}{3 - 6 x} d x