Derivative Calculator with Steps
Derivative Calculator f'(x)
Enter f(x) in the variable x. Compute the first or second derivative, then write the tangent line at x0.
The calculator above differentiates a function of one variable, simplifies the result, and can evaluate f′(x₀) and the tangent line at a point. Each step names the rule used.
Formulas used
(u ± v)′ = u′ ± v′, (uv)′ = u′v + uv′
(u/v)′ = (u′v − uv′)/v², [f(u)]′ = f′(u)·u′
Tangent: y = f′(x₀)(x − x₀) + f(x₀)
- (xⁿ)′ = n·xⁿ⁻¹, (sin x)′ = cos x, (eˣ)′ = eˣ, (ln x)′ = 1/x.
Worked example
Differentiate f(x) = x³ − 3x² + 2:
f′(x) = 3x² − 6x, f″(x) = 6x − 6
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Type the function f(x) and, optionally, the point x₀.
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.