What is the derivative of cot^3(x) ?

The derivative of cot^3(x) is -3cot^2(x)csc^2(x)

What is the first derivative of cot^3(x) ?

The first derivative of cot^3(x) is -3cot^2(x)csc^2(x)

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\frac{d}{d x} (cot^{3} (x))

- 3 cot^{2} (x) csc^{2} (x)

Solution steps

\frac{d}{d x} (cot^{3} (x))

Apply the chain rule:

3 (cot (x))^{2} \frac{d}{d x} (cot (x))

= 3 (cot (x))^{2} \frac{d}{d x} (cot (x))

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

= 3 (cot (x))^{2} (- csc^{2} (x))

Simplify

= - 3 cot^{2} (x) csc^{2} (x)

What is the derivative of cot^3(x) ?
The derivative of cot^3(x) is -3cot^2(x)csc^2(x)
What is the first derivative of cot^3(x) ?
The first derivative of cot^3(x) is -3cot^2(x)csc^2(x)