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I was trying to understand ito's lemma. When I came across the taylor series expansion of df(x).

df(x) = f'(x) dx + (1/2!) f''(x) (dx)^2 + ...

I searched everywhere for the derivation of this but couldn't find. So I tried it on my own.

f(x)= f(a) + f'(a)(x-a) + (1/2!) [f''(a)*(x-a)^2] +...

so if Itake d/dx

df(x)/dx = f'(a) + (1/2!) [f''(a)d(x-a)^2/dx] + ...

Making it

df(x)/dx = f'(a) + (1/2!) [f''(a) 2(x-a)] + (1/3!) [f''(a) 3(x-a)^2] +...

Can someone help me with how to proceed from here?

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