# Show that the function #y=1/(1+tanx)# is decreasing for all values of #x#?

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Show that the function #y=1/(1+tanx)# is decreasing for all values of #x# ?

Thanks!

Show that the function

Thanks!

##### 1 Answer

Oct 3, 2017

Start by finding the derivative.

#y = (tanx + 1)^-1#

By the chain rule, we have

#y' = -sec^2x/(tanx + 1)^2#

We immediately see that

This means that

However, with restrictions we see that

So the function is decreasing but then there are asymptotes, so just keep that in mind. Here is the graph to verify.

Hopefully this helps!