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\frac{d}{dx}\left(arcsin\left(\frac{x}{a}\right)\right)

Derive the function arcsin(x/a) with respect to x

Answer

$\frac{1}{a\sqrt{\frac{-x^2}{a^2}+1}}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(arcsin\left(\frac{x}{a}\right)\right)$
1

Taking the derivative of arcsine

$\frac{1}{\sqrt{1-\left(\frac{x}{a}\right)^2}}\cdot\frac{d}{dx}\left(\frac{x}{a}\right)$

Unlock this step-by-step solution!

Answer

$\frac{1}{a\sqrt{\frac{-x^2}{a^2}+1}}$
$\frac{d}{dx}\left(arcsin\left(\frac{x}{a}\right)\right)$

Main topic:

Differential calculus

Used formulas:

3. See formulas

Time to solve it:

~ 0.65 seconds