derivative of x/(x^2-x+25)

Lösung

\frac{d}{d x} (\frac{x}{x ^{2} - x + 25})

\frac{- x ^{2} + 25}{( x ^{2} - x + 25 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} - x + 25})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x ^{2} - x + 25 ) - \frac{d}{d x} ( x ^{2} - x + 25 ) x}{( x ^{2} - x + 25 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} - x + 25) = 2 x - 1

= \frac{1 \cdot ( x ^{2} - x + 25 ) - ( 2 x - 1 ) x}{( x ^{2} - x + 25 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x ^{2} - x + 25 ) - ( 2 x - 1 ) x}{( x ^{2} - x + 25 ) ^{2}} : \frac{- x ^{2} + 25}{( x ^{2} - x + 25 ) ^{2}}

= \frac{- x ^{2} + 25}{( x ^{2} - x + 25 ) ^{2}}

\frac{d}{d t} (t^{n} e^{a t})

\int (3 x + 4)^{2} d x

x \to 2 lim (\frac{∣ x - 2 ∣}{2 - x})

x \to 0 lim (- 2 x^{2})

in v erse l a pl a ce \frac{2}{s ( s + 2 ) ( s + 3 )}