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g(x)=xf(x), where f(x)=x"sin"(1)/(x),x!=...

`g(x)=xf(x)`, where `f(x)=x"sin"(1)/(x),x!=0=0,x=0`. At `x=0`:

A

g is differentiable but g' is continuous

B

g is differentiable but g' is not continuous

C

g is differentiable while f is not continuous

D

both f and g are differentiable.

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The correct Answer is:
A
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