Hi i am trying to find the dirivtive of (4-x^2)^(1/2). I know that i need to use u subsitution and u=4-x^2. Then i get d/dx[u^(1/2)](-2x) then i get stuck, can someone please help me?
thank you
Chain rule: $\displaystyle \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$.
$\displaystyle u = 4 - x^2$.
$\displaystyle y = u^{1/2}$.
Therefore $\displaystyle \frac{dy}{du} = \frac{1}{2} u^{-1/2} = \frac{1}{2} \frac{1}{\sqrt{u}} = \frac{1}{2} \frac{1}{\sqrt{4 - x^2}}\, $ and $\displaystyle \frac{du}{dx} = -2x$.
So $\displaystyle \frac{dy}{dx} = \frac{1}{2} \frac{1}{\sqrt{4 - x^2}} \times (-2x) = \frac{-x}{\sqrt{4 - x^2}}$.