# How do you differentiate #y = -(1/x^2) - sqrtx + (1/2)#?

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To differentiate the function ( y = -\frac{1}{x^2} - \sqrt{x} + \frac{1}{2} ), you would take the derivative of each term separately using the rules of differentiation:

- For the term ( -\frac{1}{x^2} ), use the power rule for differentiation: ( \frac{d}{dx}\left(-\frac{1}{x^2}\right) = 2x^{-3} ).
- For the term ( -\sqrt{x} ), use the power rule for differentiation and the chain rule: ( \frac{d}{dx}\left(-\sqrt{x}\right) = -\frac{1}{2\sqrt{x}} ).
- For the constant term ( \frac{1}{2} ), its derivative is zero since it has no ( x ) term.

Adding these derivatives together, you get the derivative of the function:

[ \frac{dy}{dx} = 2x^{-3} - \frac{1}{2\sqrt{x}} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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