Higher order derivatives are used in physics; for example, the first derivative with respect to time of the position of a moving object is its velocity, and the second derivative is its acceleration.

While the first derivative can tell us if the function is increasing or decreasing, the second derivative tells us if the first derivative is increasing or decreasing.

The first derivative evaluated at x 0 is illustrated as a simple slope, as is the first derivative evaluated at x 1 . You can also see that the rate of change at x 0 is larger than at x 1.

Using the Derivative to Test for Extremes The first derivative of a function tells about the general shape of the function, and we can use that shape information to determine whether an extreme point is a …

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Learn to define what first derivatives are. Learn how to find the first derivative of functions. Discover the first derivative formula and see examples.

Dec 3, 2025 · The first derivative of a function f is a single derivative of the function, denoted f^' (x). The term "first derivative" is commonly used instead of just "derivative" to distinguish it from higher-order …