Ah, to find the derivative of √x from first principles, ji, one must carefully apply the limit definition—that long formula with h going to zero. It is a bit tricky with the algebra, simplifying the numerator by multiplying by the conjugate. In my tailoring, I know the proper method is different from the quick power rule, just as a hand-stitched hem is different from a machine-finished one. But I must confess, my mind always jumps to the power rule first, just as my hands reach for the old, faltering motor even when I know the careful, slow way is the true foundation.
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