derivative of (x^2-7x+13/(x-3))

Lösung

\frac{d}{d x} (\frac{x ^{2} - 7 x + 13}{x - 3})

\frac{x ^{2} - 6 x + 8}{( x - 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 7 x + 13}{x - 3})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} - 7 x + 13 ) ( x - 3 ) - \frac{d}{d x} ( x - 3 ) ( x ^{2} - 7 x + 13 )}{( x - 3 ) ^{2}}

\frac{d}{d x} (x^{2} - 7 x + 13) = 2 x - 7

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

= \frac{( 2 x - 7 ) ( x - 3 ) - 1 \cdot ( x ^{2} - 7 x + 13 )}{( x - 3 ) ^{2}}

Vereinfache

\frac{( 2 x - 7 ) ( x - 3 ) - 1 \cdot ( x ^{2} - 7 x + 13 )}{( x - 3 ) ^{2}} : \frac{x ^{2} - 6 x + 8}{( x - 3 ) ^{2}}

= \frac{x ^{2} - 6 x + 8}{( x - 3 ) ^{2}}

y^{^{''}} - 2 y^{^{'}} = 4 t

\frac{d}{d x} (\frac{x}{10})

x \to 10 + lim (\frac{x ^{3}}{x - 10})

\int \frac{1}{x ( 1 + 2 ln ( x ) )} d x

x \to 0 lim (2 + 3 e^{\frac{1}{x}})