What is the derivative of arcsin(x^2/4)?

Nov 22, 2016

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

Explanation:

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

$\frac{d}{\mathrm{dx}} \left(\arcsin u\right) = \frac{1}{\sqrt{1 - {u}^{2}}} \cdot \frac{d}{\mathrm{dx}} \left(u\right)$

$\frac{d}{\mathrm{dx}} \left(u\right) = \frac{x}{2}$

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