Derivative Calculator
Calculate derivatives of mathematical functions symbolically with our free derivative calculator. Get step-by-step solutions for polynomial, trigonometric, logarithmic, and exponential functions.
Function Input
Supported functions: x^n, sin(x), cos(x), tan(x), ln(x), e^x, and constants
Derivative Results
Enter a function to calculate its derivative
Common Derivative Examples
Polynomial Functions
Trigonometric Functions
Logarithmic & Exponential
How to Use the Derivative Calculator
Enter Your Function
Type your mathematical function using standard notation. Examples: x^2, sin(x), cos(x), tan(x), ln(x), e^x. Use ^ for powers and parentheses for complex expressions.
Select Derivative Order
Choose whether you want the first derivative f'(x) or second derivative f''(x). First derivatives show rate of change, second derivatives show concavity.
Choose Calculation Mode
Select symbolic mode to see the derivative formula, or numerical mode to evaluate the derivative at a specific point.
Calculate and Review
Click calculate to see the derivative with step-by-step solution. Review the mathematical steps to understand the differentiation process.
Tips for Using Derivatives
Power Rule: For f(x) = x^n, the derivative is f'(x) = n·x^(n-1). This is the most fundamental derivative rule.
Chain Rule: When differentiating composite functions f(g(x)), multiply the derivative of the outer function by the derivative of the inner function.
Product Rule: For f(x) = u(x)·v(x), the derivative is f'(x) = u'(x)·v(x) + u(x)·v'(x).
Quotient Rule: For f(x) = u(x)/v(x), the derivative is f'(x) = [u'(x)·v(x) - u(x)·v'(x)]/[v(x)]².
Common Derivatives: Memorize derivatives of basic functions: sin(x) → cos(x), cos(x) → -sin(x), e^x → e^x, ln(x) → 1/x.
Second Derivatives: The second derivative f''(x) tells you about the concavity of the function and can help find inflection points.