Question

d/dx (√x) =
□ power rule (with rewriting the expression)

Explanation:

Step1: Rewrite the square - root as a power

We know that $\sqrt[4]{x}=x^{\frac{1}{4}}$. So, we need to find the derivative of $y = x^{\frac{1}{4}}$ with respect to $x$.

Step2: Apply the power rule for differentiation

The power rule states that if $y = x^n$, then $\frac{dy}{dx}=nx^{n - 1}$. Here, $n=\frac{1}{4}$. So, $\frac{d}{dx}(x^{\frac{1}{4}})=\frac{1}{4}x^{\frac{1}{4}-1}=\frac{1}{4}x^{-\frac{3}{4}}$.

Answer:

$\frac{1}{4}x^{-\frac{3}{4}}$