What is (\partial)/(\partial x)(arcsec(-x)) ?

The answer to (\partial)/(\partial x)(arcsec(-x)) is -1/(xsqrt(x^2-1))

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(\partial)/(\partial x)(arcsec(-x))

\frac{\partial}{\partial x} (arcsec (- x))

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

Solution steps

\frac{\partial}{\partial x} (arcsec (- x))

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- x) = - 1

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

Simplify

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

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

What is (\partial)/(\partial x)(arcsec(-x)) ?
The answer to (\partial)/(\partial x)(arcsec(-x)) is -1/(xsqrt(x^2-1))