derivative of (4x-12/((x-2)^2))

Lösung

\frac{d}{d x} (\frac{4 x - 12}{( x - 2 ) ^{2}})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x - 12}{( x - 2 ) ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 4 x - 12 ) ( x - 2 ) ^{2} - \frac{d}{d x} ( ( x - 2 ) ^{2} ) ( 4 x - 12 )}{( ( x - 2 ) ^{2} ) ^{2}}

\frac{d}{d x} (4 x - 12) = 4

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

= \frac{4 ( x - 2 ) ^{2} - 2 ( x - 2 ) ( 4 x - 12 )}{( ( x - 2 ) ^{2} ) ^{2}}

Vereinfache

\frac{4 ( x - 2 ) ^{2} - 2 ( x - 2 ) ( 4 x - 12 )}{( ( x - 2 ) ^{2} ) ^{2}} : \frac{4 ( - x + 4 )}{( x - 2 ) ^{3}}

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

x \to 3 - lim (3 - x)

\int x^{7} x^{4} + 3 d x

t an g e n t f (x) = \frac{3}{x + 1}, (2, 1)

y^{^{'}} = e^{- 3 x} + 2 x

\frac{d}{d x} (x (x^{2} + 1)^{10})