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

The derivative of (csc(x)^{-1}) is cos(x)

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

The first derivative of (csc(x)^{-1}) is cos(x)

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

cos (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= cos (x)

\int_{0}^{2} 2 π x (2 x - x^{2}) d x

\int cot (18 x) d x

\frac{d}{d x} (x^{2} + 10 x)

\frac{1}{( s ( s ^{2} + 1 ) )}

\frac{d}{d s} (s^{3})

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