If f (x) is known to be a differentiable function, then Lim △ x → 0 f ^ 2 (x + △ x) - f ^ 2 (x) / △ x =?
lim△x→0 f^2(x+△x)-f^2(x)/△x
=lim△x→0 [f(x+△x)+f(x)][f(x+△x)-f(x)]/△x
=f'(x)lim△x→0 f(x+△x)+f(x)
=2f'(x)f(x)
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