Question

use differentiation rules to find the derivative of the function.
f(x) = \sqrt4{x}
f(x) =

Explanation:

Step1: Rewrite function with exponent

\( f(x) = x^{1/4} \)

Step2: Apply power rule

\( f'(x) = \frac{1}{4}x^{(1/4 - 1)} \)

Step3: Simplify exponent

\( f'(x) = \frac{1}{4}x^{-3/4} \)

Answer:

\( \frac{1}{4}x^{-3/4} \) (or equivalently \( \frac{1}{4\sqrt[4]{x^3}} \))