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

Derive the function arcsin((1-1x^2)/(1+x^2)) with respect to x

Answer

$\frac{-2x\left(x^2+1\right)-2x\left(1-x^2\right)}{\left(x^2+1\right)^2\sqrt{\frac{-x^{4}+2x^2-1}{\left(x^2+1\right)^2}+1}}$

Step-by-step explanation

Problem

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

Taking the derivative of arcsine

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

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Answer

$\frac{-2x\left(x^2+1\right)-2x\left(1-x^2\right)}{\left(x^2+1\right)^2\sqrt{\frac{-x^{4}+2x^2-1}{\left(x^2+1\right)^2}+1}}$
$\frac{d}{dx}\left(arcsin\left(\frac{1-x^2}{1+x^2}\right)\right)$

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

~ 0.99 seconds