If `f(1)=3` , `f'(1)=2` , then `d/(dx)` `{logf(e^x+2x)}` at `x=0` is equal to........

Options

A. `2//3`
B. `3//2`
C. 2
D. 0

Answer

A

Explanation

Let `E = (d)/(dx) { log [f(e^(x) + 2x)]}`
` (1)/(f(e^(x) + 2x))xxf'(e^(x) + 2x )xx(d)/(dx) (e^(x)+ 2x)`
`= (f'(e^(x) + 2x))/(f(e^(x) + 2x)) xx (e^(x) + 2)`
At x = 0 ,
` E= (f'(e^(0) + 0))/(f(e^(0) + 0))xx(e^(0) + 2)`
`= (f'(1))/(f(1)) xx(1 +2) = (2)/(3) xx(3) = 2` .