Free Online Derivative Calculator
Enter a function, choose the variable, and optionally a point value to evaluate the derivative numerically.
What this online derivative calculator does
This tool helps you compute derivatives quickly and accurately. It returns the symbolic first derivative, symbolic second derivative, and can evaluate values at a specific point. If you provide a point, you also get the function value and tangent line form.
Whether you're reviewing calculus, checking homework, or building intuition about rates of change, this derivative calculator gives immediate feedback without requiring manual simplification first.
How to use the calculator
Step 1: Enter your function
Type your expression in standard math notation. Use operators like +, -, *, /, and ^ for powers.
Step 2: Choose the variable
Most problems use x, but you can use any valid variable name such as t or u.
Step 3: Add a point (optional)
If you enter a numeric point, the calculator evaluates f(variable), f'(variable), and f''(variable) at that point.
Supported function syntax
- Powers: x^3, (x+1)^5
- Trigonometric: sin(x), cos(x), tan(x)
- Exponential: exp(x)
- Logarithmic: ln(x), log(x) (natural log)
- Roots and absolute value: sqrt(x), abs(x)
- Constants: pi, e
Derivative rules quick refresher
Power rule
If f(x)=xn, then f'(x)=n·xn-1. Example: derivative of x5 is 5x4.
Product rule
For f(x)=u(x)v(x), the derivative is u'(x)v(x)+u(x)v'(x). Example: derivative of x·sin(x) is sin(x)+x·cos(x).
Chain rule
For composite functions, derivative of g(h(x)) is g'(h(x))·h'(x). Example: derivative of sin(x2) is cos(x2)·2x.
Why an online derivative calculator is useful
- Checks your hand calculations instantly
- Helps spot algebra mistakes in long expressions
- Builds intuition by evaluating slope at many points
- Supports quick iteration when modeling real systems
Common mistakes to avoid
- Forgetting multiplication signs (write 2*x, not 2x)
- Using parentheses incorrectly in nested functions
- Mixing degrees and radians for trig expressions
- Evaluating at points outside the domain (e.g., ln(x) at x ≤ 0)
Final thoughts
A strong calculus workflow combines conceptual understanding with fast verification tools. Use this online derivative calculator to validate your steps, explore behavior, and deepen your understanding of how functions change. For best results, solve by hand first, then use the calculator to confirm and learn from differences.