Differentiation (Trig Function)

[SciGuy26]

Homework Equations

Take the second derivative of:
cos(x^2)

The Attempt at a Solution

cos(x^2)

dy/du = -sin(u)
du/dx = 2x

dy/dx= -2xsin(x^2)

I don't know how to begin taking the derivative of this a second time...

 

[danago]

What rule do you think you will need to use?

 

[steelphantom]

Use the product rule with -2x and sin(x^2). You'll have to use the chain rule again when you calculate the derivative of sin(x^2).

 

[SciGuy26]

So I'd have 2xcos(u) + -2sin(u)

How am I to use the chain rule at this point?

Ugh I don't understand how combine rules with composite functions.

 

[SciGuy26]

nm...

Solution should be as follows:
-2xsin(x^2)

dy/du= sin(u)
du/dx= 2x

-2xsin(u) + -2xsin(U)

-2xcos(u) + -2sin(u)

= 2x(-2xcos(x^2) + -2sin(x^2))

Could someone please confirm? Thank you for the help.