f(x)=x1 , now to check that derivative exist or not , we know that to check the derivative of function exist or not , we apply formula -
f′(x)=lim h→0hf(x+h)−f(x)
, now limh→0 hx+h1−x1
=limh→0 hxx+hx−x+h
=limh→0 hxx+h(x+x+h)x+xx+h−x+hx−(x+h) =x251
hence we can clearly see that f'(0), of a function tends to infinity hence f'(0) does not exist .
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