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

Lösung

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

- \frac{11}{( x - 3 ) ^{2}}

Schritte zur Lösung

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

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

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

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

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

Vereinfache

\frac{3 ( x - 3 ) - 1 \cdot ( 3 x + 2 )}{( x - 3 ) ^{2}} : - \frac{11}{( x - 3 ) ^{2}}

= - \frac{11}{( x - 3 ) ^{2}}

\int \frac{1}{2 x ^{2} - 16} d x

\int \frac{4 - x ^{2}}{x} d x

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

x \to - 4 lim ((x)^{2})

\int \frac{1}{x ^{2} + 3} d x