Differentiation Problem: Find the Derivative of y = 1/ COS(t^2)

[andrey21]

Find the derivative of the following:
y = 1/ COS(t^2)

Homework Equations

Here is my attempt

Using (Cos(t^2))^-1

SOlve using the chain rule:

u = t^2
du = 2t
dy/dt = -1.(-sin(u))^(-2) .(2t)
= -2t(-sin(u))^(-2)

= -2t/(Sin(t^2))^2

Is this correct or have I totally used the wrong techiniques?

 

[phyzguy]

This isn't correct. Try applying the chain rule twice, starting with u=cos(t^2).

 

[physicsman2]

You can do it whatever way you want, but I would use the quotient rule. It seems less confusing to me.

 

[Mark44]

Your function is the same as sec(t^2). If you know the rule for the derivative of the secant function, you can use that (plus the chain rule).

 

[phyzmatix]

In light of Mark's comment, here is something useful from Paul's Online Math Notes.