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Popular Calculus >

derivative of sin^{-2}(x)

Solution

\frac{d}{d x} (sin^{- 2} (x))

Solution

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

Solution steps

\frac{d}{d x} (sin^{- 2} (x))

Simplify

sin^{- 2} (x) : csc^{2} (x)

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

Apply the chain rule:

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

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

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

= 2 csc (x) (- cot (x) csc (x))

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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