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

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Answer 1 · 2016-08-19T13:29:56

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

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

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

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

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

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