derivative of (x^2-2x-3/(x+2))

Lösung

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

\frac{x ^{2} + 4 x - 1}{( x + 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

= \frac{( 2 x - 2 ) ( x + 2 ) - 1 \cdot ( x ^{2} - 2 x - 3 )}{( x + 2 ) ^{2}}

Vereinfache

\frac{( 2 x - 2 ) ( x + 2 ) - 1 \cdot ( x ^{2} - 2 x - 3 )}{( x + 2 ) ^{2}} : \frac{x ^{2} + 4 x - 1}{( x + 2 ) ^{2}}

= \frac{x ^{2} + 4 x - 1}{( x + 2 ) ^{2}}

\int sin^{2} (v) d v

y^{^{''}} + 2 y^{^{'}} + y = sin (2 x)

\frac{d}{d x} (r (θ, x) cos (θ))

d er i v a t i v e sin (u)

d er i v a t i v e - \frac{2 x}{( x ^{2} + 1 ) ^{2}}