# Derivative Calculator

## How to use the Derivative Calculator

1. ### Type in a function to solve

To get started, type in a value of the function and click submit button. In a moment you will receive the calculation result.
2. ### See a step-by-step solution

After receiving the result, you can see a detailed step-by-step description of the solution. This will help you understand the solution of the problem.
3. ### Save the results of your calculation

After finishing, you can copy the calculation result to the clipboard, or enter a new problem to solve.

## What is Derivatives?

In math, a derivative is a way to show the rate of change or the amount that a function is changing at any given point. If you have a function f(x), there are several ways to mark the derivative of f when it comes to x. The common way that this is done is by df / dx and f'(x). If a derivative is taken n times, then the notation dnf / dxn or fn(x) is used. This term would also be considered a higher-order derivative. For second-order derivatives, it's common to use the notation f"(x). For any point where x = a, the derivative of this is f'(a) = lim(h→0) f(a+h) - f(h) / h. The limit for this derivative may not exist. If there is a limit, then f (x) will be differentiable at x = a. The function of f'(a) will be the slope of the tangent line at x=a.

To provide another example, if f(x) = x3 , then f'(x) = lim(h→0) (h+x)3 - x3 / h = 3x2 and then we can compute f''(x) : f''(x) = lim(h→0) 3(x+h)2 - 3x2 / h = 6x . When it comes to using derivatives, they serve as powerful tool with multiple uses. For example, they can be used to find inflection points, describe the motion of objects, and solve optimization problems. 