How to derive the wave equation (PDE)

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The left hand side of the equation at 1/deltax(u(x+dx, t) - u(x, t) looks like a single partial derivative (df/dx) to me, and not d2f/dx2. What am I missing?

huwcoxon
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Shouldn't it be tan(beta)-tan(alpha) at 6:17 or is there a trig property I'm not aware of? (I haven't had trig in a while so I'm just wondering)

telpurion
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Absolutely amazing.... Thank u Sir.... U explain it in easy way...

ziarehman
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Really thank you for the work, it helps :)

SEPHi.
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I did not understand the tension diagram

gemmajoy
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When delta x tends to zero, the equation becomes infinity on one hand and zero on other ffs. Youre so wrong here

mansoorimran