# How do you find the derivative of y =sqrt(2x)?

Sep 13, 2014

First, convert the square root to its exponential equivalent. Then apply the Chain and Power Rules. Next simplify the function. Lastly, convert the negative exponents back to square roots.

$y = \sqrt{2 x}$

$y = {\left(2 x\right)}^{\frac{1}{2}}$

$y ' = \left(\frac{1}{2}\right) {\left(2 x\right)}^{\left(\frac{1}{2} - 1\right)} \cdot 2$

$y ' = \left(\frac{1}{2}\right) {\left(2 x\right)}^{\left(- \frac{1}{2}\right)} \cdot 2$

$y ' = \left(\frac{2}{2}\right) {\left(2 x\right)}^{\left(- \frac{1}{2}\right)}$

$y ' = \left(1\right) {\left(2 x\right)}^{\left(- \frac{1}{2}\right)}$

$y ' = {\left(2 x\right)}^{\left(- \frac{1}{2}\right)}$

$y ' = \frac{1}{\sqrt{2 x}}$