The derivative of x2, with respect to x, is 2x. However, suppose we write x2 as the sum of x x's, and then take the derivative:
Let f(x) = x + x + ... + x (x times)
| Then f'(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 |
This argument appears to show that the derivative of x2, with respect to x, is actually x. Where is the fallacy?
Last appeared