What is the derivative of arccot(sqrt(x^2+1)) ?

The derivative of arccot(sqrt(x^2+1)) is -x/((x^2+2)sqrt(x^2+1))

What is the first derivative of arccot(sqrt(x^2+1)) ?

The first derivative of arccot(sqrt(x^2+1)) is -x/((x^2+2)sqrt(x^2+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (arccot (x^{2} + 1))

- \frac{x}{( x ^{2} + 2 ) x ^{2} + 1}

Solution steps

\frac{d}{d x} (arccot (x^{2} + 1))

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{( x ^{2} + 1 ) ^{2} + 1} \cdot \frac{x}{x ^{2} + 1} : - \frac{x}{( x ^{2} + 2 ) x ^{2} + 1}

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

What is the derivative of arccot(sqrt(x^2+1)) ?
The derivative of arccot(sqrt(x^2+1)) is -x/((x^2+2)sqrt(x^2+1))
What is the first derivative of arccot(sqrt(x^2+1)) ?
The first derivative of arccot(sqrt(x^2+1)) is -x/((x^2+2)sqrt(x^2+1))