Question

question given the function f(x)=√x, find f(x). express your answer in radical form without using negative exponents, simplifying all fractions. answer attempt 2 out of 2 f(x)=

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\sqrt{x}=x^{\frac{1}{2}}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = x^n$, then $y'=nx^{n - 1}$. For $y=x^{\frac{1}{2}}$, we have $n=\frac{1}{2}$. So $f'(x)=\frac{1}{2}x^{\frac{1}{2}-1}=\frac{1}{2}x^{-\frac{1}{2}}$.

Step3: Convert to radical form without negative exponents

Since $x^{-\frac{1}{2}}=\frac{1}{x^{\frac{1}{2}}}=\frac{1}{\sqrt{x}}$, then $f'(x)=\frac{1}{2\sqrt{x}}$.

Answer:

$\frac{1}{2\sqrt{x}}$