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

1 Answer
Jim H
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#.

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