f(x)=x^(1)/(3) , Find f^prime(x

To find the derivative of the function \( f(x) = x^{\frac{1}{3}} \), we can use the power rule for differentiation. The power rule states that if \( f(x) = x^n \), then \( f'(x) = nx^{n-1} \).<br /><br />In this case, \( n = \frac{1}{3} \). Applying the power rule, we get:<br /><br />\[ f'(x) = \frac{1}{3} x^{\frac{1}{3} - 1} \]<br /><br />Simplifying the exponent, we have:<br /><br />\[ f'(x) = \frac{1}{3} x^{-\frac{2}{3}} \]<br /><br />Therefore, the derivative of \( f(x) = x^{\frac{1}{3}} \) is \( f'(x) = \frac{1}{3} x^{-\frac{2}{3}} \).