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

Lösung

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

\frac{3 x ^{2} + 2}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d x}{d x} = 1

= \frac{( 6 x + 4 ) x - 1 \cdot ( 3 x ^{2} + 4 x - 2 )}{x ^{2}}

Vereinfache

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

= \frac{3 x ^{2} + 2}{x ^{2}}

d er i v a t i v e \frac{5}{x}

\int \frac{x}{a ^{2} + x ^{2}} d x

h \to 0 lim (4 h - h^{2})

\int \frac{9 - 162 x}{25 - 81 x ^{2}} d x

n = 0 \sum \infty (n + 1)!