Free Derivative Calculator
Enter a function in terms of x, pick the derivative order, and optionally evaluate the result at a specific point.
Supported syntax: +, -, *, /, ^, sin, cos, tan, exp, log/ln, sqrt, pi, e.
Why use a derivatives online calculator?
A derivative tells you how quickly something is changing. In mathematics, physics, economics, engineering, and data science, derivatives are used to analyze trends, optimize performance, and understand motion or growth. A reliable derivatives online calculator saves time and reduces algebra mistakes, especially when functions become long or involve multiple rules at once.
What this calculator does
- Computes the first, second, or higher-order derivative of a function.
- Returns a symbolic derivative expression in terms of
x. - Optionally evaluates both
f(x)and the derivative at a chosen point. - Supports common functions and constants used in calculus problems.
How to use it (step-by-step)
1) Enter your function
Type your function using standard calculator-style syntax, such as x^4 - 2*x + 9 or sin(x)*exp(x).
Use ^ for powers and parentheses where needed.
2) Choose derivative order
Set derivative order to 1 for the first derivative, 2 for the second derivative, and so on. Higher-order derivatives are useful for acceleration, curvature, and Taylor series work.
3) (Optional) Enter an x-value
If you provide an x-value, the tool also computes the numeric value of the derivative at that point. This is ideal for finding instantaneous rate of change.
4) Click Calculate
The result panel shows the symbolic derivative and evaluated values (if requested).
Practical applications
- Optimization: Find maximum profit, minimum cost, or best design settings.
- Physics: Velocity is the derivative of position; acceleration is the derivative of velocity.
- Economics: Marginal cost and marginal revenue are derivatives of cost and revenue functions.
- Machine learning: Gradients drive model training and parameter updates.
Common input tips
- Use
ln(x)orlog(x)for natural logarithm. - Write multiplication explicitly when unclear, e.g.,
3*x. - For trigonometric functions, angles are interpreted in radians.
- If you see an error, check parentheses and spelling of function names.
FAQ
Does this work for second derivatives?
Yes. Set derivative order to 2 (or any value up to 10 in this tool).
Can I evaluate at a specific point?
Yes. Enter a value in the x-field and the calculator returns numeric values.
Is this only for polynomials?
No. It supports many function types, including trigonometric, exponential, logarithmic, and rational expressions.