 Hi everyone! This lesson is meant to be a means for you to discover for yourself the power rule for finding derivatives. The power rule is a shortcut, an alternative to using the first limit definition of a derivative. Remember that the first limit definition yields a general expression for the derivative, for the slope of a tangent line to a given curve. So what we're trying to come up with is a way to arrive at that same answer, that same general expression, but without having to go through all that algebra that's involved in evaluating a limit. So what I have here for you are some examples. And I'm going to give you an original function, and I want you to think about how it is you work with the coefficients and exponents to get to the derivative. So suppose the first function is negative 2x squared plus 3x plus 1, the derivative is negative 4x plus 3. The second function, x squared minus 6x plus 4, its derivative is 2x minus 6. So start trying to see if you can come up with how it is you get from the original function to the derivative by working, it has something to do with the coefficients and the exponents. So if you have an original function 4 minus x squared, its derivative is negative 2x. If you simply have x cubed, that derivative is 3x squared. The derivative of 6 minus 2 thirds x is just going to be negative 2 thirds. The original function 5x squared plus 2 over x squared has a derivative of 10x minus 4 over x cubed. The function 3x cubed minus 9x has a derivative 9x squared minus 9. And finally 6 minus 7 over x to the fourth has a derivative of 28 over x to the fifth. So look these over, take a few minutes to think about it, see if you can formulate for yourself how it is you might get from an original function to its derivative. And when you think you have it, go ahead and watch the rest of this lesson.