Derivative Calculator
Differentiate with the rule spelled out at every step: power, product, quotient, and chain rule, plus second derivatives.
Runs entirely on your device - nothing is ever uploaded.
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How to use the derivative calculator
- Type f(x) with x as the variable, for example x^2 sin(x) or ln(3x).
- Press First derivative or Second derivative.
- Read the derivative, then follow the listed rules that produced it.
What it is for
Slopes and rates of change run through calculus: tangent lines, velocity from position, growth rates, and optimization all start with a derivative. Seeing which rule fired where makes the mechanics click, not just the answer.
How it works
The expression is parsed into a symbolic tree and differentiated rule by rule - sum, constant multiple, power, product, quotient, and chain - then simplified. Steps record which rule fired at each node so you can replay the derivation.
Worked example: the product rule
Differentiate x²·sin(x): the product rule gives derivative-of-first times second, plus first times derivative-of-second. That is 2x·sin(x) + x²·cos(x) - no simplification possible, and each term is labeled with the rule that made it. Chain-rule cases work the same way: for sin(3x), the outer derivative cos(3x) multiplies by the inner derivative 3, giving 3cos(3x).