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Let \( f(x+y) = f(x)f(y) \) and \( f(x) = 1 + \sin(3x)g(x) \), where \( g \) is differentiable. Then \( f'(x) \) is equal to:
Let \( f(x+y) = f(x)f(y) \) and \( f(x) = 1 + \sin(3x)g(x) \), where \( g \) is differentiable. Then \( f'(x) \) is equal to:
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The functional equation \( f(x+y)=f(x)f(y) \) characterizes exponential-type functions \( e^{cx} \). The derivative of such a function is always proportional to the function itself.
Updated On: May 1, 2026
- \( 3f(x) \)
- \( g(0) \)
- \( f(x)g(0) \)
- \( 3g(x) \)
- \( 3f(x)g(0) \)
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The Correct Option is
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