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Let f(x+y)=f(x)f(y) and f(x)=1+(sin2x)g(...

Let `f(x+y)=f(x)f(y)` and `f(x)=1+(sin2x)g(x)`, where `g(x)` is continuous. Then `f'(x)` is equal to :

A

2.g(0)

B

f(x).g(0)

C

2f(x).g(0)

D

g(0)

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The correct Answer is:
C
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