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

$y = \sqrt{x} = {x}^{\frac{1}{2}}$
Now bring the power of $\frac{1}{2}$ down as a coefficient and then subtract 1 from the current power of $\frac{1}{2}$. Evaluate the fractions and simplify. Manipulate exponents from negative to positive.
$y ' = \frac{1}{2} {x}^{\left(\frac{1}{2} - 1\right)} = \frac{1}{2} {x}^{\left(\frac{1}{2} - \frac{2}{2}\right)} = \frac{1}{2} {x}^{\left(- \frac{1}{2}\right)} = \frac{1}{2 {x}^{\frac{1}{2}}} = \frac{1}{2 \sqrt{x}}$