find the lim as h-0 (tan3(x+h)-tan3x)/h. please help thank you!!

Question

find the lim as h->0 (tan3(x+h)-tan3x)/h. please help thank you!!

turingtest · Answer

$$3\sec^23x$$but I'm guessing you want work shown using the definition of the derivative, right?

anonymous · Answer

yes please!

turingtest · Answer

*groan

Okay but this is soooooooo tedious and difficult to type. You'll have to give me a while...

turingtest · Answer

I can't do this without a lot of reference to other theorems, and it would take FOREVER. Try using this page. Look after Exercise 1 where it goes into these kinds of trig derivatives. http://tutorial.math.lamar.edu/Classes/CalcI/DiffTrigFcns.aspx Look after Exercise 1 where it goes into these kinds of trig derivatives.You can find pretty much everything you need to solve this (at least as best I can) except for the proof that d/dx(cosx)=-sinx, which you should be able to do after seeing how the proof d/dx(sinx)=cosx is done.