What is the derivative of arcsec(1/x) ?

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

What is the first derivative of arcsec(1/x) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{1}{1 - x ^{2}}

\int_{- 1}^{1} (1 - x) d x

\int \frac{x - 1}{x ^{2} + 9} d x

y^{^{''}} + 4 y^{^{'}} + 5 y = 8

- 5 x^{2} + 4

\frac{d}{d x} (6 - 5 cos (\frac{π x}{15}))

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