The best you can do is obviously [itex] f'(x_{n})\approx \frac{y_{n+1}-y_{n}}{x_{n+1}-x_{n}}[/itex].ddddd28 said:Hello,
What is the numerical formula for a derivative, considering the x's are not in the same distance?
The numerical derivative formula is a mathematical method of approximating the derivative of a function at a specific point by using nearby data points. It is often used when the exact derivative is difficult or impossible to calculate analytically.
The numerical derivative formula is typically calculated by using a finite difference method, where the derivative is approximated by the slope of a secant line between two nearby points on the function. The distance between these points, also known as the step size, can vary depending on the specific formula being used.
The numerical derivative formula requires unequal distances between data points because it is based on the slope of a secant line. If the data points were all equidistant, the secant line would become a tangent line and the formula would no longer be accurate.
The step size, or the distance between data points, is an important factor in the numerical derivative formula because it affects the accuracy of the approximation. A smaller step size will result in a more accurate derivative, but will also require more data points and computation time. A larger step size may be faster, but can lead to a less accurate approximation.
The numerical derivative formula is commonly used in many fields of science, such as physics, engineering, and economics. It allows researchers to approximate derivatives of complex functions and model real-world phenomena. It is also used in numerical optimization and solving differential equations.