derivative f(x)=(4x+2)/(4x-2)

Lösung

ableitung von

f (x) = \frac{4 x + 2}{4 x - 2}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (4 x + 2) = 4

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

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

Vereinfache

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

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

d er i v a t i v e arctan (t)

x \to - 1 lim ((x + 2)^{2})

d er i v a t i v e sin^{2} (x) cos^{2} (x)

\int x e^{3} x d x

d er i v a t i v e f (x) = (8 x + 9) (x^{3} - 6)