What is the derivative of f(x)=(arccot(x))^5 ?

The derivative of f(x)=(arccot(x))^5 is -(5arccot^4(x))/(x^2+1)

What is the first derivative of f(x)=(arccot(x))^5 ?

The first derivative of f(x)=(arccot(x))^5 is -(5arccot^4(x))/(x^2+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = (arccot (x))^{5}

- \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

Solution steps

\frac{d}{d x} ((arccot (x))^{5})

Apply the chain rule:

5 (arccot (x))^{4} \frac{d}{d x} (arccot (x))

= 5 (arccot (x))^{4} \frac{d}{d x} (arccot (x))

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

= 5 (arccot (x))^{4} (- \frac{1}{x ^{2} + 1})

Simplify

5 arccot^{4} (x) (- \frac{1}{x ^{2} + 1}) : - \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

= - \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

What is the derivative of f(x)=(arccot(x))^5 ?
The derivative of f(x)=(arccot(x))^5 is -(5arccot^4(x))/(x^2+1)
What is the first derivative of f(x)=(arccot(x))^5 ?
The first derivative of f(x)=(arccot(x))^5 is -(5arccot^4(x))/(x^2+1)