Wolfram Alpha does that pretty well and shows all the steps. Link! (Click "show steps")
I have a friend who I'm trying to help with calculus. I've been through it already, and I realize we're gonna have to apply the chain rule lots of times... but somewhere we're both screwing up. Could somebody possibly work this problem out (and show each portion)? I'd really appreciated it.
Find the derivative.
sin(sec(tan(cot(csc(cos(x))))))
The derivative of sin is cos so it is cos(sec(tan(cot(csc(cos(x)))))) times the derivative of sec(tan(cot(csc(cos(x))))).
The derivative of sec is sec*tan so the derivative of that is sec(tan(cot(csc(cos(x)))))tan(tan(cot(csc(cos(x))) )) times the derivative of tan(cot(csc(cos(x)))).
The derivative of tan is so the derivative of that is times the derivative of cot(csc(cos(x))).
The derivative of cot is so the derivative of that is times the derivative of csc(cos(x)).
The derivative of csc is -csc*cot so the derivative of that is -csc(cos(x))cot(cos(x)) times the derivative of cos(x) which is -sin(x).
Multiply all of those together to get alexmahone's answer.