derivative of (x^2-4x+3/((x-2)^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

= \frac{( 2 x - 4 ) ( x - 2 ) ^{2} - 2 ( x - 2 ) ( x ^{2} - 4 x + 3 )}{( ( x - 2 ) ^{2} ) ^{2}}

Vereinfache

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

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

\frac{d}{d x} (4 e^{- 6 x^{2}})

\int \frac{5 ( 1 - tan ^{2} ( x ) )}{sec ^{2} ( x )} d x

d er i v a t i v e x - 4

\int \frac{25 x ^{2} + 4}{x ^{4}} d x

d er i v a t i v e f (x) = ln (sin (2 x))