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

Lösung

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

- \frac{5}{( x - 3 ) ^{2}}

Schritte zur Lösung

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

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

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

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

Vereinfache

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

= - \frac{5}{( x - 3 ) ^{2}}

\frac{d}{d x} (ln^{3} (3 x^{2} - 5))

\int (x^{2} + 2)^{3} d x

x \to 0 lim ((x - 4)^{3})

y^{^{'}} = \frac{( y ^{2} + 1 )}{x}

x \to 1 lim (\frac{1 - \frac{2 l n ( 1 + x )}{x}}{x})