Derivative Calculator
Symbolic differentiation up to fourth order. Type a function of x and get the formula for f′(x), evaluated at any point.
Symbolic differentiation with the product, quotient and chain rules. Differentiates polynomials, trig, exponentials and logarithms.
What rules does the calculator know?
- Power rule: d/dx (x^n) = n·x^(n−1).
- Linearity: d/dx (af + bg) = af′ + bg′.
- Product rule: (fg)′ = f′g + fg′.
- Quotient rule: (f/g)′ = (f′g − fg′)/g².
- Chain rule applied to every composite — trig functions, exponentials, logarithms, square roots, all the standard inverses.
Higher-order derivatives
Pick "order" 2, 3, or 4 to apply the differentiation rule that many times. The calculator simplifies between each step so the output stays readable. The second derivative is what you need for the concavity test — f′′(x) > 0 means concave up, f′′(x) < 0 means concave down. Both the second-derivative test for extrema and the curvature formula in differential geometry use it.
What it cannot do (yet)
Implicit differentiation (where y is defined by an equation rather than a formula) and partial derivatives are not in this single-variable calculator. For implicit derivatives, rearrange to y = f(x) first if possible. For partial derivatives, treat the other variables as constants and use the standard rules manually.