Final Answer
$\frac{1}{2\sqrt{x}}$
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Step-by-step Solution
Problem to solve:
$\frac{d}{dx}\left(\sqrt{x}\right)$
Specify the solving method
1
The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
$\frac{1}{2}x^{\left(\frac{1}{2}-1\right)}$
Learn how to solve power rule for derivatives problems step by step online.
$\frac{1}{2}x^{\left(\frac{1}{2}-1\right)}$
Learn how to solve power rule for derivatives problems step by step online. Find the derivative d/dx(x^1/2) using the power rule. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Subtract the values \frac{1}{2} and -1. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.
Final Answer
$\frac{1}{2\sqrt{x}}$