Question

How do you find the derivative of `5ln(7x+6ln(x))`?

Answer 1

SImple: you use the chain rule!

The chain rule states that

`(dy)/(dx)=(dy)/(du)(du)/(dx)`

Thus, we just need to rename `u=7x+6ln(x)` (consequently our original function becomes `5ln(u)`), and now derivate it all part by part:

`(dy)/(du)=5*1/u`

`(du)/(dx)=7+6*1/x`

Aggregating them:

`(dy)/(dx)=5/u(7+6/x)=5/(7x+6ln(x))(7+6/x)=color(green)((35+30/x)/(7x+6ln(x)))`