What is the derivative of csc^2(x)-1 ?

The derivative of csc^2(x)-1 is -2csc^2(x)cot(x)

What is the first derivative of csc^2(x)-1 ?

The first derivative of csc^2(x)-1 is -2csc^2(x)cot(x)

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derivative of

csc^{2} (x) - 1

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

Solution steps

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

Simplify

csc^{2} (x) - 1 : cot^{2} (x)

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

Apply the chain rule:

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

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

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

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

Simplify

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

What is the derivative of csc^2(x)-1 ?
The derivative of csc^2(x)-1 is -2csc^2(x)cot(x)
What is the first derivative of csc^2(x)-1 ?
The first derivative of csc^2(x)-1 is -2csc^2(x)cot(x)