What is the derivative of arccos((10/x)) ?

The derivative of arccos((10/x)) is (10)/(xsqrt(x^2-100))

What is the first derivative of arccos((10/x)) ?

The first derivative of arccos((10/x)) is (10)/(xsqrt(x^2-100))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (arccos (\frac{10}{x}))

\frac{10}{x x ^{2} - 100}

Solution steps

\frac{d}{d x} (arccos (\frac{10}{x}))

Apply the chain rule:

- \frac{1}{1 - ( \frac{10}{x} ) ^{2}} \frac{d}{d x} (\frac{10}{x})

= - \frac{1}{1 - ( \frac{10}{x} ) ^{2}} \frac{d}{d x} (\frac{10}{x})

\frac{d}{d x} (\frac{10}{x}) = - \frac{10}{x ^{2}}

= - \frac{1}{1 - ( \frac{10}{x} ) ^{2}} (- \frac{10}{x ^{2}})

Simplify

- \frac{1}{1 - ( \frac{10}{x} ) ^{2}} (- \frac{10}{x ^{2}}) : \frac{10}{x x ^{2} - 100}

= \frac{10}{x x ^{2} - 100}

What is the derivative of arccos((10/x)) ?
The derivative of arccos((10/x)) is (10)/(xsqrt(x^2-100))
What is the first derivative of arccos((10/x)) ?
The first derivative of arccos((10/x)) is (10)/(xsqrt(x^2-100))