Question

If y=tanu, u=v-(1/v), and v=lnx, what is dy/dx at x=e?

Answer 1

So it will look like
\[y = \tan ( lnx - \frac{ 1 }{ lnx })\]

Answer 2

Holy crap man.
Well, he's the plan. Plug v into u. Plug u into y.
Derivative of tan(u) = sec^2(u)*du/dx

Answer 3

dy/dx = dy/du * du/dv *dv/dx

Answer 4

^^ Man, that's great.

Answer 5

find dy/du, du/dv, and dv/dx and then multiply the three together