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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{4}{4 - 10 x})

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

t an g e n t x^{2} + 2 x y - y^{2} + x = 5, (3, 7)

\frac{d}{d t} (t ln (t))

x \to 0 + lim (\frac{x}{ln ( x )})