y'
Definition
The derivative of a function with respect to the independent variable. It represents the rate of change of the function at any given point.
Analogy
Think of y' as a speedometer in a car. Just like how the speedometer tells you how fast you're going at any moment, y' tells you how fast a function is changing at any point.
Related terms
Tangent Line: A line that touches a curve at only one point and has the same slope as the curve at that point.
Piecewise Functions: Functions that are defined by different formulas or rules for different intervals or subdomains.
Chain Rule: A rule used to find the derivative of composite functions.
"y'" appears in:
Additional resources (1)
Practice Questions (4)
Which step of implicit differentiation involves factoring out y'?
When finding the derivative of an implicit function, what should you do with terms containing y'?
Find the particular solution to the differential equation y' = 2cos(x) with the initial condition y(0) = 3.
Given the differential equation y' = 2e^(2x), find the solution that satisfies the initial condition y(0) = 2.
Resources
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