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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d t} (cos (wt))

\int 2 e^{x} cos (x) d x

\frac{\partial}{\partial y} (e^{y})

\frac{\partial}{\partial x} (4 x y - x^{4} - y^{4} + 1)

\int_{0}^{x} e^{- t^{2}} d t

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