What is the derivative of cot(xcsc(x)) ?

The derivative of cot(xcsc(x)) is csc(x)-2csc^3(x)

What is the first derivative of cot(xcsc(x)) ?

The first derivative of cot(xcsc(x)) is csc(x)-2csc^3(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

g (x) = e^{x^{2} - x}

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

\int \frac{8}{x ln ( 5 x )} d x

n = 1 \sum \infty \frac{1}{3 n - 1}

\int \frac{1}{x ^{2} x ^{2} - 225} d x

What is the derivative of cot(xcsc(x)) ?
The derivative of cot(xcsc(x)) is csc(x)-2csc^3(x)
What is the first derivative of cot(xcsc(x)) ?
The first derivative of cot(xcsc(x)) is csc(x)-2csc^3(x)