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

Lösung

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

\frac{5}{( 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{5}{( x + 2 ) ^{2}}

= \frac{5}{( x + 2 ) ^{2}}

\frac{d y}{d x} = 3 x y

f (x) = arccos (x^{2})

s l o p e (0, - 2), (1, 2)

\frac{\partial}{\partial u} (\frac{1}{3} (v - 2 u))

\frac{\partial}{\partial x} (- y cos (6 x))