finding derivative of square roots

[jlaird77]

Having a hard time figuring out these equation y=Square root of 5x - square root of 5/x. The answer i am coming up with is the square root of 5/12x.But apparently the correct answer is 4 times the (square root of5)/10x to the power of-1/2.Whos right?

 

[mark07]

The way you wrote the question without any parenthesis, here's what I read:

\(\displaystyle \L y = \sqrt{5x} - \sqrt{\frac{5}{x}}
= \sqrt{5} \; x^{1/2} - \sqrt{5} \; x^{-1/2}
= \sqrt{5} \left( x^{1/2} - x^{-1/2} \right)\)

Now take the derivative using power rule,

\(\displaystyle \L \frac{dy}{dx} = \sqrt{5} \left( \frac{1}{2} x^{-1/2} + \frac{1}{2} x^{-3/2} \right) = \frac{\sqrt{5}}{2} \left( \frac{1}{\sqrt{x}} + \frac{1}{x\sqrt{x}} \right)\)

and simplify... If the question is different, convert radicals to powers and repeat the method.

 

[jlaird77]

Thanks, i am going to have to work on it,its been a while since i have done this kind of math,really having a hard time with the roots.

Thanks again