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?

Guest Jan 28, 2021

#1**+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! ;)

helperid1839321 Jan 28, 2021

#2**+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.

Melody Jan 28, 2021