Nov 14, 2025 · The derivative of a function is itself a function, so we can find the derivative of a derivative. For example, the derivative of a position function is the rate of change of position, or …

We know f (x) = x3, and can calculate f (x+Δx), so let's go: Use f (x) = x3: Use (x+Δx) 3 = x 3 + 3x 2 Δx + 3x (Δx) 2 + (Δx) 3. Have a play with it using the Derivative Plotter. We can use the same method to …

Just like a slope tells us the direction a line is going, a derivative value tells us the direction a curve is going at a particular spot. At each point on the graph, the derivative value is the slope of the tangent …

Jan 12, 2026 · Here are some examples of derivatives as illustration of the concept. In this, we will learn how to differentiate some commonly used functions such as sin x, cos x, tan x, sec x, cot x, …

The derivative of a function f (x) at a point x = a is the instantaneous rate of change of the function at that point. Geometrically, it represents the slope of the tangent line to the graph of f (x) at x = a.

Let us learn what exactly a derivative means in calculus and how to find it along with rules and examples. The derivative of a function f (x) is usually represented by d/dx (f (x)) (or) df/dx (or) Df …

Learn how to find the derivatives of functions in several examples with detailed solutions.

Level up on all the skills in this unit and collect up to 2,500 Mastery points! The derivative of a function describes the function's instantaneous rate of change at a certain point. Another common …

Jun 24, 2024 · In simple terms, the derivative of a function measures how the output value of a function changes as the input changes. It is often represented as the slope of the tangent line at any …

Nov 16, 2022 · Example 3 Find the derivative of the following function using the definition of the derivative. \ [R\left ( z \right) = \sqrt {5z - 8} \] First plug into the definition of the derivative as we’ve …