What is the derivative of #x*sqrt(4-x)#?
The answer is
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To find the derivative of ( x\sqrt{4-x} ), you can use the product rule. The product rule states that if you have two functions, ( f(x) ) and ( g(x) ), the derivative of their product is ( f'(x)g(x) + f(x)g'(x) ).
Let ( f(x) = x ) and ( g(x) = \sqrt{4-x} ). Then, ( f'(x) = 1 ) and ( g'(x) = -\frac{1}{2\sqrt{4-x}} ).
Applying the product rule:
[ \frac{d}{dx}(x\sqrt{4-x}) = f'(x)g(x) + f(x)g'(x) ] [ = 1 \cdot \sqrt{4-x} + x \cdot \left(-\frac{1}{2\sqrt{4-x}}\right) ] [ = \sqrt{4-x} - \frac{x}{2\sqrt{4-x}} ]
So, the derivative of ( x\sqrt{4-x} ) is ( \sqrt{4-x} - \frac{x}{2\sqrt{4-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.
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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