Скачать или смотреть Log differentiation of implicit functions | Cont. and diff. | Grade 12 | Math | Khan Academy

In this video, we learn how to perform logarithmic differentiation of implicit functions. We first look at the function x^y = y^x and then pick up (cosx)^y = (cosx)^y. In both of these, the powers can be brought down using properties of log. This is what makes logarithmeic differentiation a useful too for situations like these. Once we've dealt with the powers, we can use product rule and chain rule to perform the differentiation. Once this part is done, we can readily isolate dy/dx.

Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (https://www.khanacademy.org/math/ncer...)

Timestamps:
00:00 Find dy/dx when y^x = x^y
00:34 Taking log on both the sides
01:40 Differentiating both sides with respect to x
04:30 Find dy/dx when (cosx)^y = (cosx)^y
04:46 Taking log on both the sides
06:03 Differentiating both sides with respect to x

Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month.
Support Us: https://india.khanacademy.org/donate

Created by Ashish Gupta