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If f(x+y) = f(x).f(y) and f(x) = 1+ tan(5x) g(x) where g(x) is continuous then f¹(x) = …

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$5 f (x) . g (0)$

$5 f (x) . g^{1} (0)$

$f (x) . g^{1} (5)$

$2 f (x)$

answer is A.

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Detailed Solution

$f (x) = 1 + \tan 5 x . g (x) \Rightarrow f^{1} (x) = \tan 5 x . g^{1} (x) + g (x) . 5 s e c^{2} 5 x I f f (x + y) = f (x) . f (y) t h e n f^{1} (x) = f (x) . f^{1} (0) = f (x) (5 g (0)) = 5 . f (x) . g (0)$

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