Grah! need a bit of trig derivative help.

[Vadim]

ok, so i'm doing a calc assignment, and the whole assignment is done except for one question, the rest of the answers check properly on my graphing calculator both with nDeriv and the tangent function. this question shouldnt be so hard, but i must be missing something. could use a bit of help.

question:
y=x\tan3x+\csc^2(1-x^3), find y\prime

i've tried this one in several ways, rewriting it in terms of sin and cos, all sorts of things, and i keep coming out with essentially the same answer.

y\prime=\tan3x+3x\sec^2{3x}+6x^2\csc^2(1-x^3)\cot(1-x^3)

to me it looks right, but it doesnt check out on the calculator, so i'm assuming i'm missing something, and would appreciate a hand, cheers.

::edit:: woops, had to fix second equation, had minus instead of plus, but it still doesnt work.

[Hurkyl]

Don't forget that there are often lots of ways to write the same thing. There are a couple of things you can do:

(a) Try to do the problem in a different way and compare answers. (for instance, rewrite things in terms of sin and cos and differentiate -- this will be messy, though)
(b) Try to prove your answer and the calculator's answer are the same. (for instance, remember that \sin -x = -\sin x
(c) Try graphing y(x) and y'(x) to see if the derivative looks right.
(d) Try integrating y'(x) to see if you get y(x) + C. (probably difficult, though your calculator might be able to do it)
(e) Look for a way to numerically verify your answer. For example, remember that when h is small, y(x + h) - y(x) \approx y'(x) h. Try a dozen values of x with a small value for h. (Try to avoid x values near where y(x) is infinite)
(f) Find your own alternative way to validate your answer.

[courtrigrad]

tan(3*x)+x*(3+3*tan(3*x)^2)-3*csc^2*x^2

Try using product rule and power rule and derivatives of trigonometric functions.