Question

If `f(x) = log [e^x ((3 - x)/(3 + x))^(1/3)]`,  then `f^'(1)` is equal to

Options

• `3/4`

• `2/3`

• `1/3`

• `1/2`

Answer 1

`3/4`

Explanation:

`f(x) = log [e^x ((3 - x)/(3 + x))^(1/3)]`

= `x + 1/3 [log(3 - x) - log(3 + x)`

`f^'(x) = (7 - x^2)/(9 - x^2)`

`f^'(1) = (7 - 1)/(9 - 1) = 6/8 = 3/4`