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) = 2x + 1

Verified step by step guidance

1. Identify the function given: \( f(x) = 2x + 1 \).
2. Understand that the differential \( dy \) represents the change in \( y \) corresponding to a small change in \( x \), denoted as \( dx \).
3. To find \( dy \), we need to determine the derivative of \( f(x) \) with respect to \( x \), which is \( f'(x) \).
4. Calculate the derivative: \( f'(x) = \frac{d}{dx}(2x + 1) = 2 \).
5. Express the relationship between \( dy \) and \( dx \) using the formula \( dy = f'(x)dx \). Substitute \( f'(x) = 2 \) to get \( dy = 2dx \).