How do you find the derivative of # f(x) = 1/sqrt(x) #?
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To find the derivative of ( f(x) = \frac{1}{\sqrt{x}} ), you can use the power rule for differentiation. The power rule states that if ( f(x) = x^n ), then ( f'(x) = nx^{n-1} ). Applying this rule to the given function:
( f(x) = x^{-\frac{1}{2}} )
Using the power rule:
( f'(x) = -\frac{1}{2}x^{-\frac{1}{2}-1} )
( f'(x) = -\frac{1}{2}x^{-\frac{3}{2}} )
Simplifying:
( f'(x) = -\frac{1}{2\sqrt{x^3}} )
So, the derivative of ( f(x) = \frac{1}{\sqrt{x}} ) is ( f'(x) = -\frac{1}{2\sqrt{x^3}} ).
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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.
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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