Rational Function Derivative Calculator
Unleash the power of calculus! Easily calculate the derivative of any rational function and visualize the results.
Enter Rational Function
Type in your rational function. Use 'x' as the variable.
Example: (x^2+2x+1)/(x-1)
Derivative
Visualization
Explore the rational function and its derivative interactively on the graph below. Zoom, pan, and hover over the graph for more details.
Understanding Rational Function Derivatives
A rational function is a function that can be defined as a fraction where both the numerator and the denominator are polynomials. The derivative of a rational function tells us the rate at which the function's output value changes with respect to its input value. Calculating derivatives of rational functions is a fundamental concept in calculus, used across various fields like physics, engineering, and economics to model rates of change and optimization problems. To find the derivative of a rational function, we typically use the quotient rule, which is a method derived from the basic principles of differentiation. This tool simplifies the process, allowing you to quickly find and visualize these derivatives.
- Polynomial: An expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
- Derivative: Measures the instantaneous rate of change of a function.
- Quotient Rule: A formula used to find the derivative of a function that is the ratio of two differentiable functions.
Learn more about derivatives and rational functions on resources like Khan Academy and Paul's Online Math Notes.