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Let g(x)=xf(x), where f(x)={{:(x^(2)sin....

Let `g(x)=xf(x)`, where `f(x)={{:(x^(2)sin.(1)/(x),":",x ne0),(0,":",x=0):}`. At `x=0`,

A

g is differentiable but g' is not

B

g is differentiable while f is not differentiable

C

both f and g are non differentiable

D

g is differentiable and g' is continuous

Text Solution

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The correct Answer is:
D
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