Differentials Consider the following functions and express the relationship between a small change in x and the corresponding change in y in the form dy = f'(x)dx.


f(x) = 1/x³

Verified step by step guidance

1. Identify the function f(x) = 1/x³ and determine its derivative f'(x) using the power rule.
2. Apply the power rule: rewrite f(x) as x^(-3) and differentiate to find f'(x) = -3x^(-4).
3. Express the relationship between the small change in x (dx) and the corresponding change in y (dy) using the formula dy = f'(x)dx.
4. Substitute the expression for f'(x) into the equation: dy = -3x^(-4)dx.
5. Simplify the expression to express dy in terms of dx: dy = -3/x^4 dx.