derivative x/(x^2+13x+40)

Lösung

ableitung von

\frac{x}{x ^{2} + 13 x + 40}

\frac{- x ^{2} + 40}{( x ^{2} + 13 x + 40 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 13 x + 40})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 13 x + 40 ) - \frac{d}{d x} ( x ^{2} + 13 x + 40 ) x}{( x ^{2} + 13 x + 40 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 13 x + 40) = 2 x + 13

= \frac{1 \cdot ( x ^{2} + 13 x + 40 ) - ( 2 x + 13 ) x}{( x ^{2} + 13 x + 40 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x ^{2} + 13 x + 40 ) - ( 2 x + 13 ) x}{( x ^{2} + 13 x + 40 ) ^{2}} : \frac{- x ^{2} + 40}{( x ^{2} + 13 x + 40 ) ^{2}}

= \frac{- x ^{2} + 40}{( x ^{2} + 13 x + 40 ) ^{2}}

\int 16 + x^{2} d x

\int_{1}^{22} 1 d x

\int 8 x^{2} cos (5 x) d x

x \to 2 + lim (\frac{x}{∣ x ∣})

s l o p e (- 45) (- 4 - 8)