Instantaneous Rate of Change Example. Example question: Find the instantaneous rate of change (the derivative) at x = 3 for f(x) = x 2. Step 1: Insert the given value (x = 3) into the formula, everywhere there’s an “a”: Step 2: Figure out your function values and place those into the formula. The function is given to you in the question: for this example, it’s x 2. Choose the instant (x value) you want to find the instantaneous rate of change for. For example, your x value could be 10. Derive the function from Step 1. For example, if your function is F(x) = x^3, then the derivative would be F’(x) = 3x^2. Input the instant from Step 2 into the derivative function The Instantaneous Rate of Change Formula provided with limit exists in, When y = f(x), with regards to x, when x = a. Instantaneous Rate of Change – Solved Examples. Underneath are given the problems on Instantaneous Rate of Change: Problem 1: Compute the Instantaneous rate of change of the function f(x) = 3x 2 + 12 at x = 4 ? Answer: Known Function, f(x) = 3x 2 + 12