derivative x/(x^2+14x+45)

Lösung

ableitung von

\frac{x}{x ^{2} + 14 x + 45}

\frac{- x ^{2} + 45}{( x ^{2} + 14 x + 45 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 14 x + 45})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 14 x + 45 ) - \frac{d}{d x} ( x ^{2} + 14 x + 45 ) x}{( x ^{2} + 14 x + 45 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 14 x + 45) = 2 x + 14

= \frac{1 \cdot ( x ^{2} + 14 x + 45 ) - ( 2 x + 14 ) x}{( x ^{2} + 14 x + 45 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x ^{2} + 14 x + 45 ) - ( 2 x + 14 ) x}{( x ^{2} + 14 x + 45 ) ^{2}} : \frac{- x ^{2} + 45}{( x ^{2} + 14 x + 45 ) ^{2}}

= \frac{- x ^{2} + 45}{( x ^{2} + 14 x + 45 ) ^{2}}

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

\frac{d y}{d x} = 3 x^{2} (1 + y^{2})^{\frac{3}{2}}

d er i v a t i v e f (x) = 5 x^{2} - x^{\frac{1}{3}}

\frac{\partial}{\partial x} (e^{z})

n = 1 \sum \infty \frac{3}{2 ^{n} + 1}