What is the derivative of 5cot(2/x) ?

The derivative of 5cot(2/x) is (10csc^2(2/x))/(x^2)

What is the first derivative of 5cot(2/x) ?

The first derivative of 5cot(2/x) is (10csc^2(2/x))/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (5 cot (\frac{2}{x}))

\frac{10 csc ^{2} ( \frac{2}{x} )}{x ^{2}}

Solution steps

\frac{d}{d x} (5 cot (\frac{2}{x}))

Take the constant out:

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

= 5 \frac{d}{d x} (cot (\frac{2}{x}))

Apply the chain rule:

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

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

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

= 5 (- csc^{2} (\frac{2}{x}) (- \frac{2}{x ^{2}}))

Simplify

5 (- csc^{2} (\frac{2}{x}) (- \frac{2}{x ^{2}})) : \frac{10 csc ^{2} ( \frac{2}{x} )}{x ^{2}}

= \frac{10 csc ^{2} ( \frac{2}{x} )}{x ^{2}}

What is the derivative of 5cot(2/x) ?
The derivative of 5cot(2/x) is (10csc^2(2/x))/(x^2)
What is the first derivative of 5cot(2/x) ?
The first derivative of 5cot(2/x) is (10csc^2(2/x))/(x^2)