When finding the derivative of Y with respect to X, the first thing we want to do is simplify this. If I have a log of one base plus a log of the same base, I'm going to rewrite it as a log of a single base with the things being multiplied together. So X * X minus or X * X to the 9th is going to give us Y equal log base six of X to the 10th. We're going to bring the 10 down in front. So we get Y equal 10 log base six of X. Now log base six of X is really just 10 natural log of X divided by natural log of six. So to find the derivative, now natural log of six is just a constant. So our dy DX is going to equal 10 divided by natural log is 6 and the derivative of the natural log of X is 1 / X. Now remember if I have log base six of X, let's call it equaling some A, and I want to do a change of base formula. We would make this into six to the a power equaling X, changing it from logarithmic to exponential and then take the natural log of each side. Using the power rule we can bring that a down in front. So a natural log of 6 equal natural log of X. So A equal the natural log of X divided by the natural log of 6/6. Now way at the beginning we said that a was log base six of X. If A = 1 thing and A equals something else, then by the transitive property the two things must equal each other. So when we saw the log base six of X, we knew it was natural log of X divided by natural log of 6.