another chain rule with trig fcn's

[Guest]

Here's one with trig: (yikes)

prob is using chain rule find y = f(x) = tan(cos x).

so here's what I think:
f '(cos (x)) = -sin x
f '(tan (x)) = sec^2 x are these right?

If they are then apply chain rule:

f' = dy/dx tan(u) which = sec(u)^2

so f' = sec(u)^2 * dy/dx (u),

f' = [sec(cos(x)]^2 * dy/dx (cos x),

f' = [sec(cos(x)]^2 * (-sin (x))????? If this is right can it be simplified at all, I don't know but I don't think it can....

Thanks again guys!

 

[tkhunny]

I'm a little stunned. You performed the operation VERY formally and VERY succesfully. Why question the result? You got it.

 

[Guest]

thank you TK