`f(x) = x^(1/2) - x^(-1/2)` Use the rules of differentiation to find the derivative of the function.

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Chapter 2, Review - Problem 14 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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Note:- If y = x^n ; then dy/dx = n*x^(n-1) ; where n = constant

Now, 

`f(x) = x^(1/2) - x^(-1/2)`

`f'(x) = (1/2)*x^{(1/2)-1} - (-1/2)*x^{(-1/2)-1}`

`or, f'(x) = (1/2)*x^(-1/2) + (1/2)*x^(-3/2)`

`or, f'(x) = (1/2)*x^(-1/2)[1 + x^-1]`

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