Let f : R → R be a differentiable function with f 0 = 1 and satisfying the equation f x + y = f x f ' y + f ' x f y for all x , y ∈ R . Then, the value of log e ⁡ f 4 is

Question

Let f : R → R be a differentiable function with f 0 = 1 and satisfying the equation f x + y = f x f ' y + f ' x f y for all x , y ∈ R . Then, the value of log e ⁡ f 4 is,

MARKS App · Accepted Answer

P x , y : f x + y = f x f ' y + f ' x f y ∀ x , y ∈ R P 0,0 : f 0 = f 0 f ' 0 + f ' 0 f 0 ⇒ 1 = 2 f ' 0 ⇒ f ' 0 = 1 2 P x , 0 : f x = f x . f ' 0 + f ' x . f 0 ⇒ f x = 1 2 f x + f ' x ⇒ f ' x = 1 2 f x ⇒ f x = e 1 2 x ⇒ ln ⁡ f 4 = 2

Search any question & find its solution

Looking for more such questions to practice?