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Popular >

derivative of (sin(x)^{-1})

Solution

\frac{d}{d x} ((sin (x))^{- 1})

Solution

- cot (x) csc (x)

Solution steps

\frac{d}{d x} ((sin (x))^{- 1})

Apply the chain rule:

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

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

\frac{d}{d x} (sin (x)) = cos (x)

= - \frac{1}{( sin ( x ) ) ^{2}} cos (x)

Simplify

- \frac{1}{sin ^{2} ( x )} cos (x) : - cot (x) csc (x)

= - cot (x) csc (x)

Graph

Popular Examples

limit as x approaches-infinity of (x^3+1)/(x^2-1)

x \to - \infty lim (\frac{x ^{3} + 1}{x ^{2} - 1})

taylor 1/((1-x)^2)taylor

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

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\int \frac{3 cos ( ln ( x ) )}{x} d x

derivative of arctan(4^x)

\frac{d}{d x} (arctan (4^{x}))

derivative of ln(x-2+(x-3)/(x-2))

\frac{d}{d x} (ln (x - 2) + \frac{x - 3}{x - 2})

Frequently Asked Questions (FAQ)

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