for an antiderivative you raise the power, then divide by that new power. the 4 had a power of 0 (there was no x) so we raised it to a power of one, which made the x appear. we also divide by that new power (1), which is just 4x again. For the x^2, you raise it to x^3, then divide by that 3, so x^3/3. It's the opposite of the derivative, if you do the derivative of 4x, you lower the x's power to 0, which becomes 1, and then 4 times 1 is just 4. derivative of x^2 means you take the 2 down, becomes 2x^2, then you lower the 2 to a 1, 2x

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