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

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To differentiate ( f(x) = \sqrt{x+1} ), you can use the power rule for differentiation, which states that if ( f(x) = x^n ), then ( f'(x) = nx^{n-1} ). Applying this rule to ( f(x) = \sqrt{x+1} ), you get:

[ f'(x) = \frac{d}{dx} \sqrt{x+1} = \frac{1}{2\sqrt{x+1}} \cdot \frac{d}{dx} (x+1) ] [ = \frac{1}{2\sqrt{x+1}} \cdot 1 = \frac{1}{2\sqrt{x+1}} ]

So, the derivative of ( f(x) = \sqrt{x+1} ) is ( f'(x) = \frac{1}{2\sqrt{x+1}} ).

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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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