Thread: Trigonometric differentiation help!

Hi, I'm having a lot of trouble solving the following question related to trig differentiation. I would greatly appreciate any help.

1) Differentiate

Thanks

-2(sinx)tan(cosx)[sec(cosx)]^2

Originally Posted by nikhil

-2(sinx)tan(cosx)[sec(cosx)]^2

Yes, I'm pretty sure thats the answer..Would you mind sharing a bit of the working?

d/dx (tan(cosx))^2
= 2tan(cosx)[d/dx(tan(cosx))]
=2tan(cosx)(sec(cosx))^2(d/dx (cosx))
=2tan(cosx)(sec(cosx))^2(-sinx)
=-2(sinx)tan(cosx)(sec(cosx))^2

Nikhil used the chain rule.

Let u= cos(x),[/tex]v= tan(u)[/tex], and

Then , , and

The chain rule says

.

Of course, nikhil did it with specifically writing out "u", "v", and "w".