derivative of 2csc^2(xcot(x))

Lösung

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

4 csc^{2} (x) - 6 csc^{4} (x)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = csc^{2} (x), g = cot (x)

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

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

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

= 2 ((- 2 csc^{2} (x) cot (x)) cot (x) + (- csc^{2} (x)) csc^{2} (x))

Vereinfache

2 ((- 2 csc^{2} (x) cot (x)) cot (x) + (- csc^{2} (x)) csc^{2} (x)) : 4 csc^{2} (x) - 6 csc^{4} (x)

= 4 csc^{2} (x) - 6 csc^{4} (x)

\frac{d}{d x} (\frac{4 x ^{\frac{2}{3}}}{x ^{2} + 1})

\int \frac{1}{( x + 1 ) x ^{2} + 2 x - 15} d x

x \to 3 + lim (\frac{2}{x ^{2} - 9})

d er i v a t i v e \frac{e ^{x}}{5 x ^{6}}

x \to - 3 lim (2 x^{2} + 3 x)