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

1 Answer

Aug 19, 2016

#-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))#

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