How to use this calculator
Enter an expression and the variable to differentiate, then select the derivative order. A first derivative describes the rate of change; a second derivative describes how that rate changes. Compare the result with the original expression and its domain.
Method and interpretation
For a power x^n, the first derivative is n*x^(n-1). Higher-order differentiation applies differentiation repeatedly. Constants differentiate to zero. Symbolic rules apply only where the original function and resulting expression are defined.
Assumptions and limits
The supported symbolic engine handles many common expressions, but its output is not a proof of every domain condition or branch choice. The selected order is bounded to avoid excessive work. Graphs and rounded numeric values are illustrations; do not infer behavior outside a sampled interval from the plot alone.
Worked example
For x^3, the first derivative is 3*x^2, the second derivative is 6*x and the third derivative is 6. At x = 2, the first derivative is 12, representing the local slope of x^3.