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40 ezgo differential diagram

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First of all, I would like to clarify that my title is *slightly* clickbait. Whilst I didn't strictly record notes every single lesson about every single thing, I still did the questions my teachers told me to and virtually all homework. Also consider this post an AMA, happy to answer every and all questions around VCE, my subjects or the UCAT test (3230). Hello everyone, my name is u/robloxprostitute (@exy on discord iykyk) and I have been a long time lurker of the r/VCE subreddit. Over my VC... ok, I have 3 functions: u(z) v(x,t) z(x,t) and im looking at the case where v(x,t)=u(z) where z=x-ct im trying to write ∂v/∂t and ∂^2 v/ ∂x^2 in terms of. for ∂v/∂t ( [using this tree diagram](https://imgur.com/xGMwwAj) ) I can sa that because v(x,t) and u(z) are equal ∂v/∂t is equal to du/dz \*∂z/∂t. since ∂z/∂t=-c then ∂v/∂t=-c \*du/dz my problem is in figuring out ∂^2 v/ ∂x^2. using the same method as before Ive found ∂v/∂x=du/dz but then I dont know how to find the 2nd patial deri...