How to differentiate a function?

Let's look at the function y = 3x^2 + 6x + 3. Differentiating it gives us the derivative of y: dy/dx = 6x + 6. The original function has three terms. Let's look at each term:

1. 3x^2 (^2 means to the power of 2). This becomes 6x, because we take the index 2, multiply it by the coefficient 3, and subtract 1 from the index.
2. 6x becomes 6, because we again multiply the index by the coefficient and subtract one from the index. This gives us 6x^0, but anything to the power of 0 equals 1, so we are left with just 6.
3. 3 is removed altogether, because it doesn't have an x attached to it.