derivative of cot^2(xcsc(x))

Lösung

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

- 2 csc^{3} (x) cot (x) - cot^{3} (x) csc (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

(- 2 csc^{2} (x) cot (x)) csc (x) + (- cot (x) csc (x)) cot^{2} (x) : - 2 csc^{3} (x) cot (x) - cot^{3} (x) csc (x)

= - 2 csc^{3} (x) cot (x) - cot^{3} (x) csc (x)

\int x sin (6 x^{2} + 2) d x

\int \frac{1}{x ^{2} yz} d x

t a y l or ln (4 - 3 x)

x y^{2} y^{^{'}} = x + 3

\int x^{3} ln (x^{3}) d x