1. The problem statement, all variables and given/known data Given that the stretched length of a string is Δx(1+1/2(dy/dx)^2) show that the potential energy per unit length is equal to 1/2F(dy(x,t)/dx)^2 2. Relevant equations potential energy = kx^2 cos(kx-wt) idk really... 3. The attempt at a solution The fact that the stretched length equals Δx(1+1/2(dy/dx)^2) can be derived from the fact that the strings stretched length is equal to (x^2+x(dy/dx)^2)^1/2 and then simplified with binomial expansion. according to my answer key, the first step to the solution of solving potential energy per unit length is understanding that it is equal to (FΔx(1+1/2(dy/dx)^2)-Δx) / Δx The part about this step that I don't understand is why is the -Δx term in the numerator? Wouldn't the work per unit length just equal (Force * the amount it is stretched / Δx)? which would equal FΔx(1+1/2(dy/dx)^2) / Δx. yeah.. I don't understand why the -Δx is in the numerator i guess sums up my concerns.