derivative of (2x/(9-cot(x)))

Lösung

\frac{d}{d x} (\frac{2 x}{9 - cot ( x )})

\frac{2 ( 9 - cot ( x ) - x csc ^{2} ( x ) )}{( 9 - cot ( x ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x}{9 - cot ( x )})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{x}{9 - cot ( x )})

Wende die Quotientenregel an:

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

= 2 \cdot \frac{\frac{d x}{d x} ( 9 - cot ( x ) ) - \frac{d}{d x} ( 9 - cot ( x ) ) x}{( 9 - cot ( x ) ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (9 - cot (x)) = csc^{2} (x)

= 2 \cdot \frac{1 \cdot ( 9 - cot ( x ) ) - csc ^{2} ( x ) x}{( 9 - cot ( x ) ) ^{2}}

Vereinfache

2 \cdot \frac{1 \cdot ( 9 - cot ( x ) ) - csc ^{2} ( x ) x}{( 9 - cot ( x ) ) ^{2}} : \frac{2 ( 9 - cot ( x ) - x csc ^{2} ( x ) )}{( 9 - cot ( x ) ) ^{2}}

= \frac{2 ( 9 - cot ( x ) - x csc ^{2} ( x ) )}{( 9 - cot ( x ) ) ^{2}}

(3 x^{2} - 6 x y) d x - (3 x^{2} + 2 y) d y = 0

x \to π lim (x + sin (x))

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

d er i v a t i v e \frac{3 x}{x ^{2} - 6}

\int x sin (5 b x) d x