What is the derivative of $arcsin (3 - x^{2})$ $arcsin(3-x^2)$ ?

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Answer 1 · 2015-06-07T23:34:14

The derivative for $arcsin u$ $arcsinu$ is:

$\frac{d}{d x} [arcsin u (x)] = \frac{1}{\sqrt{1 - u^{2}}} \cdot \frac{d u (x)}{d x}$ $d/(dx)[arcsinu(x)] = 1/(sqrt(1-u^2))*(du(x))/(dx)$

$\frac{d}{d x} [arcsin (3 - x^{2})] = \frac{1}{\sqrt{1 - {(3 - x^{2})}^{2}}} \cdot (- 2 x)$ $d/(dx)[arcsin(3-x^2)] = 1/(sqrt(1-(3-x^2)^2))*(-2x)$

$= - \frac{2 x}{\sqrt{1 - {(3 - x^{2})}^{2}}}$ $= -(2x)/(sqrt(1-(3-x^2)^2))$

What is the derivative of arcsin(3-x^2)arcsin(3−x2)arcsin(3-x^2)?