Question

How do you find the derivative of `y=tan(3x)`?

Answer 1

`(dy)/(dx)=3sec^2 3x`

Explanation:

we use teh chain rule

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

`y=tan3x`

`u=3x=>(du)/(dx)=3`

`:color(red)(y=tanu=>(dy)/(du)=sec^2u)`

`(dy)/(dx)=color(red)(sec^2u)xx3`

`(dy)/(dx)=3sec^2u=3sec^2 3x`