\( 1 \leftarrow \begin{array}{l}\text { Find } g^{\prime}(x) \text { for } g(x)=x^{6 / 5} \\ g^{\prime}(x)=\square\end{array} \)

To find the derivative \( g^{\prime}(x) \) of the function \( g(x) = x^{6/5} \), we apply the power rule. According to the power rule, if \( g(x) = x^n \), then \( g^{\prime}(x) = n \cdot x^{n-1} \). Here, \( n = \frac{6}{5} \). Thus, \[ g^{\prime}(x) = \frac{6}{5} \cdot x^{\frac{6}{5} - 1} = \frac{6}{5} \cdot x^{\frac{1}{5}}. \] So, \[ g^{\prime}(x) = \frac{6}{5} x^{1/5}. \] And there you have it! Just a bit of math magic to make sense of derivatives!