Why can derivative be written as f '(a) = LIM (x → a) f (x) - f (a) / x-a Shouldn't it be written as f '(x) = LIM (△ x → 0) (x + Δ x) - f (x) / Δ x? I hope you can help me

Why can derivative be written as f '(a) = LIM (x → a) f (x) - f (a) / x-a Shouldn't it be written as f '(x) = LIM (△ x → 0) (x + Δ x) - f (x) / Δ x? I hope you can help me

Then according to f '(x) = LIM (△ x → 0) [f (x + △ x) - f (x)] / △ x
When x is a, f '(a) = LIM (△ x → 0) [f (a + △ x) - f (a)] / △ X
So let △ x = x-a
Then when △ x → 0, x-a → 0, that is, X → a
So f '(a) = LIM (x → a) [f (a + x-a) - f (a)] / (x-a)
=f'(a)=lim(x→a)[f(x)﹣f(a)]/(x-a)
Satisfied, please accept, thank you~