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Popular >

derivative of arcsec(x/2)

Solution

\frac{d}{d x} (arcsec (\frac{x}{2}))

Solution

\frac{2}{x x ^{2} - 4}

Solution steps

\frac{d}{d x} (arcsec (\frac{x}{2}))

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( \frac{x}{2} ) ^{2} ( \frac{x}{2} ) ^{2} - 1} \cdot \frac{1}{2} : \frac{2}{x x ^{2} - 4}

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

Graph

Popular Examples

integral of 1-5/3 x^{2/3}

\int 1 - \frac{5}{3} x^{\frac{2}{3}} d x

integral from 0 to pi/2 of sin(3x)

\int_{0}^{\frac{π}{2}} sin (3 x) d x

derivative of 3^{1/2}

\frac{d}{d x} (3^{\frac{1}{2}})

limit as n approaches infinity of e^{-n}ln(n)

n \to \infty lim (e^{- n} ln (n))

integral of x+3

\int x + 3 d x

Frequently Asked Questions (FAQ)

What is the derivative of arcsec(x/2) ?
The derivative of arcsec(x/2) is 2/(xsqrt(x^2-4))
What is the first derivative of arcsec(x/2) ?
The first derivative of arcsec(x/2) is 2/(xsqrt(x^2-4))