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

1 Answer
Apr 12, 2015

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.