Partial derivative of a longitudinal wave displacement function

[Zorodius]

My physics book gives this function for the displacement of a wave element oscillating in a longitudinal wave. Later on, they take the partial derivative with respect to time, like so.

My question: Did my brain fall out, or is the negative sign in the second picture not supposed to be there? I'm open to either possibility right now

 

[HallsofIvy]

You are correct. You get one negative from the $kx-\omega t$ and another from the derivative of cosine.

 

[Gokul43201]

My question: Did my brain fall out, or is the negative sign in the second picture not supposed to be there? I'm open to either possibility right now

Don't be. Understand your basics well enough that you know when something's right and when it's wrong. Your brain is doing good...just needs to feel more confident, and confidence comes from familiarity.

 

[Zorodius]

Thanks for your replies!