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

Find the derivative of arcsin(x/a)+((a^2-1x^2)^0.5)/x

Answer

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

Step-by-step explanation

Problem

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

The derivative of a sum of two functions is the sum of the derivatives of each function

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

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Answer

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

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

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

~ 6.13 seconds