derivative (2x+6)/(x+9)

Lösung

ableitung von

\frac{2 x + 6}{x + 9}

\frac{12}{( x + 9 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x + 6}{x + 9})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x + 6 ) ( x + 9 ) - \frac{d}{d x} ( x + 9 ) ( 2 x + 6 )}{( x + 9 ) ^{2}}

\frac{d}{d x} (2 x + 6) = 2

\frac{d}{d x} (x + 9) = 1

= \frac{2 ( x + 9 ) - 1 \cdot ( 2 x + 6 )}{( x + 9 ) ^{2}}

Vereinfache

\frac{2 ( x + 9 ) - 1 \cdot ( 2 x + 6 )}{( x + 9 ) ^{2}} : \frac{12}{( x + 9 ) ^{2}}

= \frac{12}{( x + 9 ) ^{2}}

x \to 0 lim (\frac{1}{x} - cot (x))

\int x \cdot e^{3 x^{2}} d x

\frac{d}{d x} (tan (x^{3} + 1))

d er i v a t i v e f (x) = (- x^{2} + 3)^{2}

d er i v a t i v e f (x) = (x + 2) (2 x^{2} - 3)