en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of arcsin(a/x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of (x^3-2x^2+5x-2)/(x^3-2x^2+x)

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

derivative of-2sin^2(x)

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

derivative of 4x^2+x+1

\frac{d}{d x} (4 x^{2} + x + 1)

sum from n=1 to infinity of ((ln(3n)))/n

n = 1 \sum \infty \frac{( ln ( 3 n ) )}{n}

derivative of (2x^3+3)^6 derivative of

(2 x^{3} + 3)^{6}

Frequently Asked Questions (FAQ)

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