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

The derivative of csc(sqrt(x^2-1)) is -(xcot(sqrt(x^2-1))csc(sqrt(x^2-1)))/(sqrt(x^2-1))

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

The first derivative of csc(sqrt(x^2-1)) is -(xcot(sqrt(x^2-1))csc(sqrt(x^2-1)))/(sqrt(x^2-1))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

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