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Can the product rule be applied if one of the functions is not differentiable? For example,
f(x)={g(x)sin(1/x), x not =0
=0, x=0
where g(0)=g'(0)=0.
f'(0)=g'(0)sin(1/0) + g(0)dsin(1/x)/dx
=0sin1/0+0dsin(1/x)/dx=0?
applying the limit definition, I get
f'(0)=g'(0)lim sin(1/h) where h-->0
is this zero?
f(x)={g(x)sin(1/x), x not =0
=0, x=0
where g(0)=g'(0)=0.
f'(0)=g'(0)sin(1/0) + g(0)dsin(1/x)/dx
=0sin1/0+0dsin(1/x)/dx=0?
applying the limit definition, I get
f'(0)=g'(0)lim sin(1/h) where h-->0
is this zero?