Derivatives of a Constant in a Trigonometric Function

[Jani08]

Homework Statement

Find y'' if y=1/3(1+cos^2(√x))

Homework Equations

The Attempt at a Solution

Now I believe I got the first derivative right since the teacher marked ir right, but my real question here is what do I do with the 1/3? Is it ok to throw away the constant when I see derivative and just worry bout the other the thing in the parenthesis?

y'=1/3(cox√x)(-sin√x)(1/√x)
y''=??

 

[enricfemi]

Yes, it is ok.

 

[enricfemi]

if a is a constant
y=a*f(t)
then
dy/dt=a*df/dt