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A comment on What’s Wrong with “Multiplication Is Repeated Addition”? (2008).
x^2 = x * x = x + x ... + x (x times)
Therefore,
d/dx(x^2) =
d/dx(x * x) =
d/dx (x + x + ... + x (x times)) =
d/dx(x) + d/dx(x) + ... + d/dx(x) (x times) =
1 + 1 + ... + 1 (x times) =
x
x^2 = x * x = x + x ... + x (x times)
Therefore,
d/dx(x^2) =
d/dx(x * x) =
d/dx (x + x + ... + x (x times)) =
d/dx(x) + d/dx(x) + ... + d/dx(x) (x times) =
1 + 1 + ... + 1 (x times) =
x