1. We start with the given function: $$y = 7\cos(x^6) - \frac{1}{8}$$ 2. To find the derivative, we differentiate each term separately. The derivative of a constant is zero, so the derivative of \(-\frac{1}{8}\) is 0. 3. For the term \(7\cos(x^6)\), we use the chain rule. The derivative of \(\cos u\) with respect to \(u\) is \(-\sin u\), and the derivative of \(x^6\) with respect to \(x\) is \(6x^5\). 4. Applying the chain rule: $$\frac{dy}{dx} = 7 \times -\sin(x^6) \times 6x^5 = -42 x^5 \sin(x^6)$$ 5. So, the derivative is: $$y' = -42 x^5 \sin(x^6)$$