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Popular >

derivative of f(x)=(arccot(x))^5

Solution

derivative of

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

Solution

- \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}

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Frequently Asked Questions (FAQ)

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)