Question

Find the differential in y=3√6x

Answer 1

$\bold {Answer}$

$y^{'} = \dfrac {3\sqrt{6}}{2\sqrt{x}} = \dfrac {3\sqrt{6x}}{2x}$

$\bold {Solution }$

$y = 3\sqrt{6x}$

$= 3\sqrt{6} × \sqrt{x}$

$y^{'} = \dfrac {d}{dx}(3\sqrt{6x})$

$= 3\sqrt{6}\dfrac {d}{dx}(\sqrt{x})$

$= 3\sqrt{6}\dfrac {d}{dx}(x^{\small\dfrac {1}{2}})$

$= \dfrac {1}{2} × 3\sqrt{6} × x ^{\small-\dfrac{1}{2}})$

$= \dfrac {3\sqrt{6}}{2\sqrt{x}}$ Or $\dfrac {3\sqrt {6x}}{2x}$