JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

Let

f\left( {x + y} \right) = f\left( x \right)f\left( y \right)

and

f\left( x \right) = 1 + \left( {\sin 2x} \right)g\left( x \right)

where

g\left( x \right)

is continuous. Then,

f'\left( x \right)

equals

View answer and explanation

Correct option: B

2f\left( x \right)g\left( 0 \right)

Option B (

2f\left( x \right)g\left( 0 \right)

) is correct because it is the result of applying the limit definition of the derivative and using the given functional equation.

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