derivative of (x-5/((x-3)(x-1)))

Lösung

\frac{d}{d x} (\frac{x - 5}{( x - 3 ) ( x - 1 )})

\frac{- x ^{2} + 10 x - 17}{( x - 3 ) ^{2} ( x - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 5}{( x - 3 ) ( x - 1 )})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 5 ) ( x - 3 ) ( x - 1 ) - \frac{d}{d x} ( ( x - 3 ) ( x - 1 ) ) ( x - 5 )}{( ( x - 3 ) ( x - 1 ) ) ^{2}}

\frac{d}{d x} (x - 5) = 1

\frac{d}{d x} ((x - 3) (x - 1)) = 2 x - 4

= \frac{1 \cdot ( x - 3 ) ( x - 1 ) - ( 2 x - 4 ) ( x - 5 )}{( ( x - 3 ) ( x - 1 ) ) ^{2}}

Vereinfache

\frac{1 \cdot ( x - 3 ) ( x - 1 ) - ( 2 x - 4 ) ( x - 5 )}{( ( x - 3 ) ( x - 1 ) ) ^{2}} : \frac{- x ^{2} + 10 x - 17}{( x - 3 ) ^{2} ( x - 1 ) ^{2}}

= \frac{- x ^{2} + 10 x - 17}{( x - 3 ) ^{2} ( x - 1 ) ^{2}}

\int sin^{5} (\frac{x}{3}) cos (\frac{x}{3}) d x

\int_{- 3}^{1} (x^{2} + 2 x - 3) d x

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

d er i v a t i v e e^{θ}

t a y l or y = ln (1 + x)