Question

How do you find the derivative of $y=\sqrt{x}$?

Answer 1

Convert the square root to its exponential form and then use the power rule.
$y=\sqrt{x}=x^{\frac{1}{2}}$
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.
$y^{\prime }=\frac{1}{2}{x}^{(\frac{1}{2}-1)}=\frac{1}{2}{x}^{(\frac{1}{2}-\frac{2}{2})}=\frac{1}{2}{x}^{(-\frac{1}{2})}=\frac{1}{2x^{\frac{1}{2}}}=\frac{1}{2\sqrt{x}}$