derivative of (x^3/(3-6x^2+8x-7))

Lösung

\frac{d}{d x} (\frac{x ^{3}}{3 - 6 x ^{2} + 8 x - 7})

- \frac{x ^{2} ( 3 x ^{2} - 8 x + 6 )}{2 ( 3 x ^{2} - 4 x + 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3}}{3 - 6 x ^{2} + 8 x - 7})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{3} ) ( 3 - 6 x ^{2} + 8 x - 7 ) - \frac{d}{d x} ( 3 - 6 x ^{2} + 8 x - 7 ) x ^{3}}{( 3 - 6 x ^{2} + 8 x - 7 ) ^{2}}

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

\frac{d}{d x} (3 - 6 x^{2} + 8 x - 7) = - 12 x + 8

= \frac{3 x ^{2} ( 3 - 6 x ^{2} + 8 x - 7 ) - ( - 12 x + 8 ) x ^{3}}{( 3 - 6 x ^{2} + 8 x - 7 ) ^{2}}

Vereinfache

\frac{3 x ^{2} ( 3 - 6 x ^{2} + 8 x - 7 ) - ( - 12 x + 8 ) x ^{3}}{( 3 - 6 x ^{2} + 8 x - 7 ) ^{2}} : - \frac{x ^{2} ( 3 x ^{2} - 8 x + 6 )}{2 ( 3 x ^{2} - 4 x + 2 ) ^{2}}

= - \frac{x ^{2} ( 3 x ^{2} - 8 x + 6 )}{2 ( 3 x ^{2} - 4 x + 2 ) ^{2}}

\frac{d}{d x} (\frac{20 x ^{2}}{( x - 1 ) ^{3}})

t an g e n t f (x) = \frac{1}{( 2 x - 1 ) ^{6}}, at x = 1

x \to - 2 lim (8 + x^{3})

\frac{d}{d a} (\frac{cos ^{2} ( a )}{1 - sin ( a )})

\frac{d}{d x} (\frac{4 x}{( x ^{2} + 1 )})