Question

Find the derivatives of the following functions at the indicated points.
$y=\ln (2-\sqrt{2x+1}),y^{\prime }\left(0\right)=?$

Answer 1

$y=ln(2-\sqrt{2x+1})$

To find : $y^{\prime }\left(0\right)=?$

$y^{\prime }=\frac{1}{2-\sqrt{2x+1}}\left[\frac{-2}{2\sqrt{2x+1}}\right]$

$=\frac{-1}{(2-\sqrt{2x+1})\left(\sqrt{2x+1}\right)}$

Now $y^{\prime }\left(0\right)=\frac{-1}{(2-\sqrt{1})\left(\sqrt{1}\right)}$

$=\frac{-1}{(2-1)}=-1$.