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

To differentiate \( y = (7x - 8)^{14} \), we can apply the chain rule. The chain rule states that if you have a composition of functions, you take the derivative of the outer function multiplied by the derivative of the inner function. Here, the outer function is \( u^{14} \) and the inner function is \( u = 7x - 8 \). First, find the derivative of the outer function: \[ \frac{dy}{du} = 14u^{13} \] Then, find the derivative of the inner function: \[ \frac{du}{dx} = 7 \] Now, applying the chain rule: \[ \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} = 14(7x - 8)^{13} \cdot 7 \] Simplifying that gives: \[ y' = 98(7x - 8)^{13} \] So, \( y' = 98(7x - 8)^{13} \).