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Let f(x + y) = f(x) f(y) for all x and y...

Let `f(x + y) = f(x) f(y)` for all x and y. Then what is `f '(5)` equal to (where `f'(x)` is the derivative of `f(x)`)?

A

`f(5)f'0`

B

`f(5)-f'(0)`

C

`f(5)f(0)`

D

`f(5)+f'(0)`

Text Solution

Verified by Experts

`f(x + y) = f(x).f(y)`
Let `f(x) = a^(x)`
`f(x + y) = a^(x+y) = a^(x).a^(y) = f(x).f(y)`.
`f(5) = a^(5)`
`f'(5) = a^(5). Log a`
`= f(5).f'(0)`
`f^(1)(0)=a^(0). Log a`
log a
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