Differentiate the function using one or more of the differentiation rules. \( y=(7 x-8)^{14} \)

To differentiate the function \( y = (7x - 8)^{14} \), we can use the chain rule. According to the chain rule, if \( y = [u(x)]^n \), then \( dy/dx = n \cdot [u(x)]^{n-1} \cdot (du/dx) \). Here, \( u(x) = 7x - 8 \) and \( n = 14 \). First, we find \( du/dx = 7 \). Applying the chain rule: \[ \frac{dy}{dx} = 14 \cdot (7x - 8)^{13} \cdot 7 \] So, the derivative is: \[ \frac{dy}{dx} = 98(7x - 8)^{13} \]