How do you differentiate f(x)=x * (4-x^2)^(1/2) using the chain rule?

Feb 6, 2017

$\frac{\mathrm{dy}}{\mathrm{dx}} = - {x}^{2} {\left(4 - {x}^{2}\right)}^{- \frac{1}{2}} + {\left(4 - {x}^{2}\right)}^{\frac{1}{2}}$
$y = x \cdot {\left(4 - {x}^{2}\right)}^{\frac{1}{2}}$
$\mathrm{dy} \mathrm{dx} = x \cdot \left[\frac{1}{2} {\left(4 - {x}^{2}\right)}^{- \frac{1}{2}} \left(- 2 x\right)\right] + \left[{\left(4 - {x}^{2}\right)}^{\frac{1}{2}} \left(1\right)\right]$
$\frac{\mathrm{dy}}{\mathrm{dx}} = - {x}^{2} {\left(4 - {x}^{2}\right)}^{- \frac{1}{2}} + {\left(4 - {x}^{2}\right)}^{\frac{1}{2}}$