 In this final video for lecture 26, I wanna compute the derivative of the function y equals x times the absolute value of x. Now it turns out that absolute value of x can oftentimes cause a lot of trouble when you try to calculate its derivative, but if you use logarithmic differentiation, we can avoid a lot of that trouble. And the main reason is if you take the derivative of the natural log of x, that's equal to one over x, but if you take the derivative of the natural log of the absolute value of x, that doesn't change the formula whatsoever. So using natural logs, we can actually avoid some of the confusion, complication that would come from these absolute values here. So if we take the natural log of the absolute value of y on the left, and we do that for the right as well, the natural log of the absolute value of x times the absolute value of x right here, you can then expand the right-hand side, which would become the natural log here of the absolute value of x plus the natural log of the absolute value of the absolute value of x, right? Double absolute value doesn't really make much of a difference once you switch to be positive, it'll just be positive again. So you get the absolute value of x, this becomes two times the natural log of the absolute value of x, this is important. Then when we take the derivative of both sides with respect to x, the left-hand side will become y prime over y, like it always does with logarithmic differentiation. The right-hand side will then become two over x times both sides by y, you get y prime equals two y over x, but why is x times the absolute value of x? So you get two times the x times the absolute value of x over x, for which then the x's cancel out and we see that the derivative here is just two times the absolute value of x. So with effortless ease, we can compute derivatives involving absolute values if we employ logarithmic differentiation. And that will then conclude for us lecture 26. If you have any questions, feel free to post them in the comments of any of these videos, I'll be glad to answer them as soon as I get an opportunity. If you learned something, hit a like button. If you wanna see more videos like this, subscribe to see them and hopefully I'll see you some other time. Bye everyone.