Let f x is a differentiable function on x ∈ R , such that f x + y = f x f y for all x , y ∈ R where f 0 ≠ 0 . If f 5 = 10 , f ' 0 = 6 , then the value of f ′ 5 is equal to

Question

Let f x is a differentiable function on x ∈ R , such that f x + y = f x f y for all x , y ∈ R where f 0 ≠ 0 . If f 5 = 10 , f ' 0 = 6 , then the value of f ′ 5 is equal to,

MARKS App · Accepted Answer

f ′ 5 = lim h → 0 f 5 + h − f 5 h = l i m h → 0 f 5 + h - f 5 + 0 h = l i m h → 0 f 5 . f h - f 5 . f 0 h [ ∵ f x + y = f x . f y f o r a l l x , y ] = l i m h → 0 f h - f 0 h . f 5 = f ′ 0 . f 5 = 6 × 10 = 60

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