derivative of csc(x(x+cot(x)))

Lösung

\frac{d}{d x} (csc (x) (x + cot (x)))

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

Schritte zur Lösung

\frac{d}{d x} (csc (x) (x + cot (x)))

Wende die Produktregel an:

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

f = csc (x), g = x + cot (x)

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

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

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

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

Vereinfache

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

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

d er i v a t i v e 2 sin (x^{2})

x \to \infty lim (- 10 e^{- 2 x})

\frac{d y}{d t} = \frac{y}{2}

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

\frac{d}{d x} (3000 (1 + \frac{4 x}{x ^{2} + 100}))