Final Answer
$\frac{\frac{1}{2}}{\sqrt{x}}$
Step-by-step Solution
Problem to solve:
$\frac{d}{dx}\left(\sqrt[]{x}\right)$
Solving method
1
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
$\frac{1}{2}x^{-\frac{1}{2}}$
2
Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number
$\frac{\frac{1}{2}}{\sqrt{x}}$
Final Answer
$\frac{\frac{1}{2}}{\sqrt{x}}$