derivative (7x^2+1)/(x^2+5)

Lösung

ableitung von

\frac{7 x ^{2} + 1}{x ^{2} + 5}

\frac{68 x}{( x ^{2} + 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7 x ^{2} + 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} ( 7 x ^{2} + 1 ) ( x ^{2} + 5 ) - \frac{d}{d x} ( x ^{2} + 5 ) ( 7 x ^{2} + 1 )}{( x ^{2} + 5 ) ^{2}}

\frac{d}{d x} (7 x^{2} + 1) = 14 x

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

= \frac{14 x ( x ^{2} + 5 ) - 2 x ( 7 x ^{2} + 1 )}{( x ^{2} + 5 ) ^{2}}

Multipliziere aus

14 x (x^{2} + 5) - 2 x (7 x^{2} + 1) : 68 x

= \frac{68 x}{( x ^{2} + 5 ) ^{2}}

\frac{d}{d x} (7 cot (x))

x \to \infty lim (\frac{4}{x ^{2}})

\frac{d y}{d x} = e^{y}

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

f (x) = 4 - 2 x - 2