Question

How do you differentiate `sqrt(1+(1/x))`?

Answer 1

`-1/(2x^2sqrt(1+1/x))`

Explanation:

`f(x) = sqrt(1+1/x) = (1+1/x)^(1/2)`

`f'(x) = 1/2 (1+1/x)^(-1/2) * d/dx(1+1/x)` (Power rule and Chain rule)

`f'(x) = 1/(2sqrt(1+1/x)) *(0-1/x^2)` (Power rule)

`f'(x) = -1/(2x^2sqrt(1+1/x))`