Final answer:
To find the second derivative of y = 1/x⁶ with respect to x, differentiate the function twice using the power rule.
Step-by-step explanation:
To find the second derivative of y with respect to x, we need to differentiate y twice with respect to x. Let's start with the given function y = 1/x⁶.
First derivative: dy/dx = d(1/x⁶)/dx. Using the power rule, we get dy/dx = -6/x⁷.
Second derivative: d²y/dx² = d(-6/x⁷)/dx. Applying the power rule again, we obtain d²y/dx² = 42/x⁸.