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

Lösung

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

\frac{- 3 x ^{2} + 10 x + 21}{( x ^{2} + 7 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Multipliziere aus

3 (x^{2} + 7) - 2 x (3 x - 5) : - 3 x^{2} + 10 x + 21

= \frac{- 3 x ^{2} + 10 x + 21}{( x ^{2} + 7 ) ^{2}}

\frac{d}{d x} (- 12 e^{- 2 x})

x \to 3 lim (\frac{3 x - 9}{x - 3})

\frac{d}{d x} (\frac{tan ( x )}{x ^{3}})

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

\int \frac{sec ^{2} ( \frac{1}{x ^{5}} )}{x ^{6}} d x