derivative (x^3)/(6x-3)

Lösung

ableitung von

\frac{x ^{3}}{6 x - 3}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3}}{6 x - 3})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (6 x - 3) = 6

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

Vereinfache

\frac{3 x ^{2} ( 6 x - 3 ) - 6 x ^{3}}{( 6 x - 3 ) ^{2}} : \frac{x ^{2} ( 4 x - 3 )}{3 ( 2 x - 1 ) ^{2}}

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

a re a 3 x^{2} + 4, [1, 2]

d er i v a t i v e 160 + 3.2 x - 0.03 x^{2}

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

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

n = 0 \sum \infty \frac{2}{3} n (\frac{1}{3})^{n}