About this tool
The Taylor / Maclaurin Series Calculator is a free, in-browser calculus tool that expands a function f(x) as a power series about a center point a. When a = 0 this is the Maclaurin series. It uses the same symbolic differentiation engine as the Derivative tool to compute successive derivatives f, f', f'', … and evaluates each one at the center to build the coefficients cₖ = f⁽ᵏ⁾(a) / k!, forming the polynomial Pₙ(x) = Σ cₖ·(x − a)ᵏ.
Everything runs locally in your browser, so nothing you enter is uploaded. Choose the center a (default 0) and the number of terms n, and the calculator returns the simplified Taylor polynomial in ascending powers together with a term-by-term table listing k, the k-th derivative value f⁽ᵏ⁾(a), and its coefficient cₖ. The factorial in each denominator is computed iteratively. You can type the usual operators, ^ for powers, parentheses, the constants pi and e, and functions like sin, cos, exp, ln and sqrt.
Familiar expansions come straight out: exp(x) about 0 gives 1 + x + x²/2 + x³/6 + …, sin(x) gives x − x³/6 + x⁵/120 − …, and 1/(1 − x) gives 1 + x + x² + …. If the function or one of its derivatives is undefined at the chosen center (for instance ln(x) at a = 0), the tool reports invalid input, since the series cannot be built there. This mirrors the Taylor-series pages of Symbolab and eMathHelp.