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How do I solve the derivative of \(y = \frac{(1-\sqrt{x})(1+\sqrt{x})}{\sqrt{x}}\)
i got it to \(y = \frac{1-x}{x^{0.5}}\)

Then to get the derivative I did to \(y’ = \frac{1-1}{0.5x^{-0.5})}{}\)

And that equals to 0 but it says it was the wrong answer, how do I solve this?

 Jan 28, 2021
 #1
avatar+580 
+1

If you rewrite your second equation as (1-x)x^0.5, you'll notice it doesn't actually equal the same thing. That's because it was in the bottom of a fraction before, meaning it should have a *negative* derivative.
Also, you forgot about all constants turning into 0 when you take the derivative, meaning the derivative should look a bit more like (0-1)(-0.5)(x^-1.5).

Hope this is able to help! ;)

 Jan 28, 2021
 #2
avatar+112575 
+1

Here is one suggestion:

 

\(y = \frac{1-x}{x^{0.5}}\\ y = \frac{1}{x^{0.5}}- \frac{x}{x^{0.5}}\\ y=x^{-0.5}-x^{0.5}\\ y'=-0.5x^{-1.5}-0.5x^{-0.5}\\ y'=\frac{-0.5}{x\sqrt x }-\frac{0.5}{\sqrt x}\\ y'=\frac{-1}{2x^{1.5}}(1+x) \)

 

It probably would have been quicker to use the quotient rule.

Note: I have not checked for careless errors.

 Jan 28, 2021

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