I am still contemplating over this proble, so if anyone is out there who can help me thanks. Suppose that the function f is diﬀerentiable at a. Prove (without

quoting a theorem) that f 2 is diﬀerentiable at a.

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- November 12th 2006, 08:30 PMSwamifezSuppose f is differentiable at a.
I am still contemplating over this proble, so if anyone is out there who can help me thanks. Suppose that the function f is diﬀerentiable at a. Prove (without

quoting a theorem) that f 2 is diﬀerentiable at a. - November 12th 2006, 08:38 PMSoltras
- November 12th 2006, 08:50 PMSwamifez
f squared is what i meant.

- November 12th 2006, 10:36 PMsrinivas
f is differentiable at a implies that f'(a) = [f(a+h) - f(a)]/h as h->0

take g(x) = [f(x)]^2

therefore lim h->0 [[f(a+h)]^2 - [f(a)]^2 ]/h = f'(a) * [f(a+h)+f(a)]

and u can easily see that the second bracket is equal to 2*f(a) as h->0

so the square of f is differentiable at a and the derivative is 2f(a)*f'(a)