derivative f(2)=(3x+2)/(x-1)

Lösung

ableitung von

f (2) = \frac{3 x + 2}{x - 1}

- \frac{5}{( x - 1 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{3 ( x - 1 ) - 1 \cdot ( 3 x + 2 )}{( x - 1 ) ^{2}} : - \frac{5}{( x - 1 ) ^{2}}

= - \frac{5}{( x - 1 ) ^{2}}

\int sin^{4} (3 x) cos^{2} (3 x) d x

\frac{\partial}{\partial x} ((8 + 23 x) y^{t a n (x)})

f (t) = ln (t^{2} + 3)

x \to 0 lim (\frac{1 + 7 x - 1 - 5 x}{x})

t an g e n t f (x) = \frac{1}{x ^{6}}, (3, \frac{1}{729})