Math Help - help finding the dirivative

1. help finding the dirivative

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

2. Originally Posted by cowboys111
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: $\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$.

$u = 4 - x^2$.

$y = u^{1/2}$.

Therefore $\frac{dy}{du} = \frac{1}{2} u^{-1/2} = \frac{1}{2} \frac{1}{\sqrt{u}} = \frac{1}{2} \frac{1}{\sqrt{4 - x^2}}\,$ and $\frac{du}{dx} = -2x$.

So $\frac{dy}{dx} = \frac{1}{2} \frac{1}{\sqrt{4 - x^2}} \times (-2x) = \frac{-x}{\sqrt{4 - x^2}}$.

3. awesome! thank you