derivative of (x^2-7x+6/(x^2+7))

Lösung

\frac{d}{d x} (\frac{x ^{2} - 7 x + 6}{x ^{2} + 7})

\frac{7 x ^{2} + 2 x - 49}{( x ^{2} + 7 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 7 x + 6}{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} - 7 x + 6 ) ( x ^{2} + 7 ) - \frac{d}{d x} ( x ^{2} + 7 ) ( x ^{2} - 7 x + 6 )}{( x ^{2} + 7 ) ^{2}}

\frac{d}{d x} (x^{2} - 7 x + 6) = 2 x - 7

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

= \frac{( 2 x - 7 ) ( x ^{2} + 7 ) - 2 x ( x ^{2} - 7 x + 6 )}{( x ^{2} + 7 ) ^{2}}

Multipliziere aus

(2 x - 7) (x^{2} + 7) - 2 x (x^{2} - 7 x + 6) : 7 x^{2} + 2 x - 49

= \frac{7 x ^{2} + 2 x - 49}{( x ^{2} + 7 ) ^{2}}

\int e^{- r t} d t

(sin (2 θ))^{^{'}}

h \to 0 lim (\frac{sin ( h )}{7 h})

y \to 0 lim (\frac{5}{y ^{2} + y} - \frac{5}{y})

\int_{3}^{\infty} \frac{1}{x ^{2} - 1} d x