What is the derivative of ln(arccsc(x)) ?

The derivative of ln(arccsc(x)) is -1/(arccsc(x)sqrt(x^2)\sqrt{x^2-1)}

What is the first derivative of ln(arccsc(x)) ?

The first derivative of ln(arccsc(x)) is -1/(arccsc(x)sqrt(x^2)\sqrt{x^2-1)}

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derivative of

ln (arccsc (x))

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

Solution steps

\frac{d}{d x} (ln (arccsc (x)))

Apply the chain rule:

\frac{1}{arccsc ( x )} \frac{d}{d x} (arccsc (x))

= \frac{1}{arccsc ( x )} \frac{d}{d x} (arccsc (x))

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

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

Simplify

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

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

\frac{\partial}{\partial y} (x^{3} y^{5})

y^{^{'}} = \frac{x - 2}{y - 4}

f (x) = x^{2} + 9, at x = - 4

\int x os (x) d x

n = 1 \sum \infty \frac{e ^{n}}{n}

What is the derivative of ln(arccsc(x)) ?
The derivative of ln(arccsc(x)) is -1/(arccsc(x)sqrt(x^2)\sqrt{x^2-1)}
What is the first derivative of ln(arccsc(x)) ?
The first derivative of ln(arccsc(x)) is -1/(arccsc(x)sqrt(x^2)\sqrt{x^2-1)}