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A function f : R to R Satisfies the f...

A function f : ` R to R ` Satisfies the following conditions
(i) `f (x) ne 0 AA x in R `
(ii) `f(x +y)= f(x) f(y) AA x, y, in R `
(iii) f(x) is differentiable
(iv ) f'(0) =2
The derivative of f(x) satisfies the equation

A

f'(x +y) =f'(x) + f'(y)

B

f'(x +y) = f'(x) `xx` f'(y)

C

f'(x+y) = f'(x ) f(y)

D

f'(x +y) = f'(x) + f(y)

Text Solution

Verified by Experts

The correct Answer is:
B
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