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How do you find the derivative of # 2^(1/2) (x + 2)#?

Answer 1

Samantha Adkison

#sqrt2#

First, I would distribute the #2^(1/2)# I prefer to call it #sqrt(2)#:

#sqrt2x+2sqrt(2)#

Now, use the power rule :

#sqrt2#

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Answer 2

Luke Alvarez

To find the derivative of (2^{\frac{1}{2}} (x + 2)), you can use the power rule and the chain rule. The derivative is (2^{\frac{1}{2}}) times the derivative of ((x + 2)) plus ((x + 2)) times the derivative of (2^{\frac{1}{2}}). The derivative of (x + 2) is (1), and the derivative of (2^{\frac{1}{2}}) is (\frac{1}{2} \cdot 2^{\frac{1}{2} - 1}), which simplifies to (\frac{1}{2} \cdot 2^{-\frac{1}{2}}). Therefore, the derivative is (2^{\frac{1}{2}}) plus ((x + 2) \cdot \frac{1}{2} \cdot 2^{-\frac{1}{2}}).

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Answer from HIX Tutor

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.