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Popular >

derivative of arcsec(x/a)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral from-infinity to 0 of 1/(5-8x)

\int_{- \infty}^{0} \frac{1}{5 - 8 x} d x

derivative of x^2sec(1/(x^3))

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

integral of (x^3)/(x^8+5)

\int \frac{x ^{3}}{x ^{8} + 5} d x

(\partial)/(\partial x)(e^{2y}(3e^y-2x))

\frac{\partial}{\partial x} (e^{2 y} (3 e^{y} - 2 x))

inverse oflaplace (s+1)/((s+6)^2*(s+2))inverse laplace

\frac{s + 1}{( s + 6 ) ^{2} \cdot ( s + 2 )}

Frequently Asked Questions (FAQ)

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