What is the derivative of cot^5(x) ?

The derivative of cot^5(x) is -5cot^4(x)csc^2(x)

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

The first derivative of cot^5(x) is -5cot^4(x)csc^2(x)

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derivative of

cot^{5} (x)

- 5 cot^{4} (x) csc^{2} (x)

Solution steps

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

Apply the chain rule:

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

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

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

= 5 (cot (x))^{4} (- csc^{2} (x))

Simplify

= - 5 cot^{4} (x) csc^{2} (x)

What is the derivative of cot^5(x) ?
The derivative of cot^5(x) is -5cot^4(x)csc^2(x)
What is the first derivative of cot^5(x) ?
The first derivative of cot^5(x) is -5cot^4(x)csc^2(x)