#Deriving wave equation

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golden imp
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Hi! I am attempting to derive the wave equation (classical physics) and having trouble understanding this step. I have not taken differential equations, but I do have a highschool understanding of derivatives and integrals --- wondering if anyone can explain what's going on here. This is the video it's from: https://www.youtube.com/watch?v=CifQ-BhBQSA. Timestamp is 5:20.

Screenshot_2024-01-30_213824.png
YouTube
Faculty of Khan
Introducing the Wave Equation: Derivation and Intuition

In this video, I introduce the Wave Equation. I carry out a derivation of the Wave Equation for a 1-D string by using force balances and applying a small amplitude approximation. I also give some of the intuition of the wave equation to give a better idea of what it means, kind of like what I did with the Heat Equation here: https://www.youtube....

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cinder trellisBOT
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golden imp
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(btw: I understand the left bit --- as delta(x) approaches 0 the slope becomes more and more tangental and eventually you get the derivative. It's the right side of the equation I don't understand).