Difference Quotient Calculator

This tool simplifies the difference quotient (f(x + h) - f(x)) / h for a polynomial in x. Enter the function and it expands f(x + h) with the binomial theorem, cancels f(x), divides by h and prints the simplified quotient together with its limit as h approaches zero, which is the derivative. A second action evaluates the quotient at a value of x and a step size h, showing the secant slope beside the tangent slope and the gap between them. The working is exact arithmetic on exponents rather than a numerical estimate, so a very small h loses no accuracy. Only polynomials are accepted; trigonometric, exponential, logarithmic and root terms are refused rather than approximated.