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

Lösung

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

\frac{6}{( x + 3 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int_{0}^{1} \frac{37}{4 y - 1} d y

\int_{0}^{3} arctan (x) d x

\frac{\partial}{\partial x} (- sin (x) - sin (2 y))

d er i v a t i v e f (x) = \frac{x ^{2}}{7 + x}

x y^{^{'}} - 2 y = 2 y x^{2}