Expert: Paul Klarreich - 10/20/2005

Question
find dy/dt.

1) y=(1 + cot(t/2))^-2
2) y= (1 + tan^4 (t/12))^3

Answer
Hi, Amy,

By now you should see how to set these up as extended chain rule examples.

1) y= (1 + cot(t/2))^-2
Write  y = u^-2,

and u = 1 + cot v,

and v = t/2

Get the three derivatives, multiply them, eliminate, and you are home.


2) y= (1 + tan^4 (t/12))^3   

Set  y = u^3

    u = 1 + v^4

    v = tan(w)

    w = t/12

I think you know the drill now.  (At the end, eliminate the w first, then the v, then the u.)