derivative of (x^2-6x+12/(x-4))

Lösung

\frac{d}{d x} (\frac{x ^{2} - 6 x + 12}{x - 4})

\frac{x ^{2} - 8 x + 12}{( x - 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 6 x + 12}{x - 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} - 6 x + 12 ) ( x - 4 ) - \frac{d}{d x} ( x - 4 ) ( x ^{2} - 6 x + 12 )}{( x - 4 ) ^{2}}

\frac{d}{d x} (x^{2} - 6 x + 12) = 2 x - 6

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

= \frac{( 2 x - 6 ) ( x - 4 ) - 1 \cdot ( x ^{2} - 6 x + 12 )}{( x - 4 ) ^{2}}

Vereinfache

\frac{( 2 x - 6 ) ( x - 4 ) - 1 \cdot ( x ^{2} - 6 x + 12 )}{( x - 4 ) ^{2}} : \frac{x ^{2} - 8 x + 12}{( x - 4 ) ^{2}}

= \frac{x ^{2} - 8 x + 12}{( x - 4 ) ^{2}}

\int 24 x^{2} d x

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

\int x^{2} + 5 x + 6 d x

2 sin (x), 3 cos (x), x = 0, x = 0.7 π

\int (11 x + 12 x) d x