Question

How do you differentiate the function `y=tan[ln(ax + b)]`?

Answer 1

Here you have a function (`tan`) of a function (`ln`) of a function (`ax+b`).
You can use the Chain Rule where you derive each function leaving the "nested" one as it is and multiply the derivative together.
So you get:
`tan(x)` derived gives you: `1/cos^2(x)`
`ln(x)` derived gives you: `1/x`
`ax+b` derived gives you: `a`.

So finally:
`y'=1/(cos^2(ln(ax+b)))*1/(ax+b)*a`

This can also be written as

`y'=(asec^2(ln(ax+b)))/(ax+b)`