# Derivatives of Composite Natural Log Functions with the Chain Rule

## Метаданные

- **Канал:** The Organic Chemistry Tutor
- **YouTube:** https://www.youtube.com/watch?v=nE_IPKGWqt4

## Содержание

### [0:00](https://www.youtube.com/watch?v=nE_IPKGWqt4) Segment 1 (00:00 - 02:00)

Number 62, find dy over dx. So in order to find that, first we need to find the derivative using this formula. The derivative of u to the n is going to be n u raus 1 * u prime. So dydx is going to equal n is 5 and then times u. U is going to be everything inside the brackets. So the natural log of 7x cub + 8 and then this is going to be raised to the n -1 5 - 1 is 4 and then time u prime. So the derivative of ln 7xqub + 8. So to find the derivative of that we need to use this formula. It's going to be u prime over u where this u prime is different from that u prime. So the derivative of what's inside the derivative of 7 x cub + 8 that's going to be 7 * the derivative of x cub which is 3x^2. The derivative of 8 is 0 / what's inside of ln. So that's 7 x cub + 8. Now the only thing we can really do to simplify this is we could multiply five, 7 and 3 together and just put it in one fraction. So we can write the final answer as 7 * 3 is 21 * 5 that's going to be 105. And then we have x^2 ln 7 x cub + 8 and this is raised to the 4th power and this is all divided by 7 xq + 8. So that's going to be the final answer for this particular problem.

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*Источник: https://ekstraktznaniy.ru/video/41233*