Question

What is the derivative of `(tanx-1)/secx`?

Answer 1

It is `cosx+sinx`.

You could use the quotient rule and then try to simplify. That's probably how a machine would do it. But we are human, we can think about how to do this.

`(tanx-1)/secx = tanx/secx - 1/secx=(sinx/cosx)/(1/cosx) - 1/ (1/cosx)`

So the expression is equal to:

`(tanx-1)/secx = sinx- cosx`

And the derivative is `cosx+sinx`.