derivative f(x)=(6x+16)/(x+3)

Lösung

ableitung von

f (x) = \frac{6 x + 16}{x + 3}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{6 x + 16}{x + 3})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 6 x + 16 ) ( x + 3 ) - \frac{d}{d x} ( x + 3 ) ( 6 x + 16 )}{( x + 3 ) ^{2}}

\frac{d}{d x} (6 x + 16) = 6

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

= \frac{6 ( x + 3 ) - 1 \cdot ( 6 x + 16 )}{( x + 3 ) ^{2}}

Vereinfache

\frac{6 ( x + 3 ) - 1 \cdot ( 6 x + 16 )}{( x + 3 ) ^{2}} : \frac{2}{( x + 3 ) ^{2}}

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

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

d er i v a t i v e 4 e^{4 x} cos (5 x)

t a y l or \frac{1}{1 - x - x ^{2}}, 0

n = 0 \sum \infty 4546644

x \to 3 lim ((x^{x} + x)^{x})