derivative of (4x^2-3/(x-1))

Lösung

\frac{d}{d x} (\frac{4 x ^{2} - 3}{x - 1})

\frac{4 x ^{2} - 8 x + 3}{( x - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x ^{2} - 3}{x - 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 4 x ^{2} - 3 ) ( x - 1 ) - \frac{d}{d x} ( x - 1 ) ( 4 x ^{2} - 3 )}{( x - 1 ) ^{2}}

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

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

= \frac{8 x ( x - 1 ) - 1 \cdot ( 4 x ^{2} - 3 )}{( x - 1 ) ^{2}}

Vereinfache

\frac{8 x ( x - 1 ) - 1 \cdot ( 4 x ^{2} - 3 )}{( x - 1 ) ^{2}} : \frac{4 x ^{2} - 8 x + 3}{( x - 1 ) ^{2}}

= \frac{4 x ^{2} - 8 x + 3}{( x - 1 ) ^{2}}

\frac{d}{d t} ((sin (t) + cos (t))^{2})

s l o p e y = 5 x^{2} + \frac{6}{x}

d er i v a t i v e y = \frac{8 t}{8 + t}

x \to 2 lim (2 x e^{x^{2}})

\int 2 x^{3} (1 - x^{4})^{- \frac{1}{4}} d x