derivative of (x^2-8x+7/(x^2+9))

Lösung

\frac{d}{d x} (\frac{x ^{2} - 8 x + 7}{x ^{2} + 9})

\frac{8 x ^{2} + 4 x - 72}{( x ^{2} + 9 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 8 x + 7}{x ^{2} + 9})

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 + 7 ) ( x ^{2} + 9 ) - \frac{d}{d x} ( x ^{2} + 9 ) ( x ^{2} - 8 x + 7 )}{( x ^{2} + 9 ) ^{2}}

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

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

= \frac{( 2 x - 8 ) ( x ^{2} + 9 ) - 2 x ( x ^{2} - 8 x + 7 )}{( x ^{2} + 9 ) ^{2}}

Multipliziere aus

(2 x - 8) (x^{2} + 9) - 2 x (x^{2} - 8 x + 7) : 8 x^{2} + 4 x - 72

= \frac{8 x ^{2} + 4 x - 72}{( x ^{2} + 9 ) ^{2}}

\frac{\partial}{\partial x} (t^{2} e^{x} + 3 x^{2})

x \to 2 lim (x^{2} + x - 6)

\int_{0}^{π} sin^{3} (x) d x

in v erse l a pl a ce \frac{( 2 s + 1 )}{s ( 2 s + 10 )}

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