What is the derivative of $arcsin (\frac{x^{2}}{4})$ $arcsin(x^2/4)$ ?

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Answer 1 · 2016-11-22T01:49:04

$\frac{d}{d x} (arcsin (\frac{x^{2}}{4})) = \frac{x}{2 \sqrt{1 - \frac{x^{4}}{16}}}$ $d/dx(arcsin(x^2/4)) = x/(2sqrt(1-x^4/16))$

Let $u = \frac{x^{2}}{4}$ $u=x^2/4$

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

$\frac{d}{d x} (u) = \frac{x}{2}$ $d/dx(u) = x/2$

The rest is just plugging in and multiplying $u$ $u$ .

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