Question

find derivative q=square root of 2r - (r^2) , find dq/dr? using chain rule

Answer 1

Given:

$q = \sqrt{2r - r^{2} }$.

To Find:

$dq/dr = ?$

Solution:

According to question,

                 $\dfrac{dq}{qr} = \dfrac{d(\sqrt{2r - r^{2} } )}{dr} \\ = \dfrac{1(2 - 2r)}{2\sqrt{2r - r^{2} } } } \\ = \dfrac{1 - r}{\sqrt{2r - r^{2} } }$

Hence,

          $\dfrac{dq}{dr} = \dfrac{1 - r}{\sqrt{2r - r^{2} } } .$