What is a derivative?
The derivative f′(x) measures how fast a function changes: it is the slope of the tangent line at each point. Instead of using the limit definition every time, you combine a handful of rules. This calculator shows which rule applies at each step.
The main derivative rules
Worked example
Find the derivative of f(x) = x² sin(x). It is a product, so use the product rule with u = x² and v = sin(x). Then u′ = 2x and v′ = cos(x), so f′(x) = 2x·sin(x) + x²·cos(x).
Frequently asked questions
How do I enter my function?
Type it with x as the variable. Use ^ for powers (x^3), * or a space for multiplication (3x or 3*x), and parentheses for function inputs: sin(x), ln(x), sqrt(x), e^(2x). log(x) means log base 10 and ln(x) is the natural log.
Which rules does the calculator show?
The power, constant multiple, sum and difference, product, quotient and chain rules, plus the derivatives of trig, inverse trig, exponential and logarithmic functions.
Is the answer checked?
Yes. Every answer is checked numerically at several points against an independent symbolic derivative, so the steps and the final answer always agree.
Can it do higher-order derivatives?
Paste the first derivative back into the box to get the second derivative, and repeat for higher orders.