Question

silly silly question, what is the second derivative of cos(x)?

Answer 1

the first derivative is -sin(x) but then where to go from there?

Answer 2

Hmmm if you're getting confused by this, one thing you can try to remember is that you can simply pull constant coefficients outside of the derivative that you want to take. Not always necessary, but maybe it'll help you get a feel for it.

(-sinx)' = -(sinx)'

So what's the derivative of sinx, then throw a negative in front of it: D

Answer 3

Find its first derivative first...

Answer 4

\[\frac{d}{dx}(\cos(x)) = -\sin(x)\]

Answer 5

Now, to find second derivative, you must differentiate it one more time..

\[\frac{d}{dx}(-\sin(x)) = - \frac{d}{dx}(\sin(x)) = ??\]

Answer 6

Now, do you know the derivative of sin(x) ??

Answer 7

indeed cos(x)
therefore it will end up being -cos(x)

Answer 8

Thank both of you! that is what I had a hunch it would come to but I didn't want to get it wrong... completely spaced it but I'm working on a linear approximation problem, so this will work perfect!

Answer 9

Yep it will end up at -cos(x)..

Great...

Answer 10

I feel silly, thank you for this. I'm sure ill get some other silly questions that google wont help out with sometime soon... sigh

Answer 11

Basically we write it as :

\[\frac{d^2}{dx^2}(\cos(x)) = - \cos(x)\]