Free Online derivative calculator - first order differentiation solver step-by-step

Learn how to find a derivative using the first principle (Δ / delta method) in this beginner-friendly lesson. We’ll go step by step, starting from the definition of a derivative and carefully ...

Dec 11, 2025 · Afterwards, we will dive deeper into why the derivative approximations presented on this page are valid and how accurate they are, making use of Taylor series expansions.

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.

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

Pretty cool, right? How to find the first derivative Now that we know why we need them, let’s learn how to find first derivatives! We’ll walk through some detailed examples together.

To find the derivative of this function, we simply need to use the Power Rule. The Power rule states that for each term, we simply multiply the coefficient by the power to find the new coefficient. We then …

Graphing by hand is tedious and imprecise. Even the use of a graphing program will only give us an approximation for the locations and values of maxima and minima. We can use the first derivative of 𝑓, …

The first derivative test helps in finding the turning points, where the function output has a maximum value or a minimum value. Let us learn more about the first derivative test, steps for the 1st …

The first derivative of a point is the slope of the tangent line at that point. When the slope of the tangent line is 0, the point is either a local minimum or a local maximum.