Product/Quotient Rules. Please Help Check My Work

[dalasTR]

I hope these attachements work, and I apologize for size errors.
I am about half way done with my homework tonight, but so far I have encountered problems such as the three here that I need help with. My work is included in regards to how far I have gotten. Thanks in advance to any help.

 

[DrMike]

For the first one, it's easier to simplify first before you differentiate :

\(\displaystyle \frac{2x+5}{\sqrt{x}}=\frac{2x+5}{x^{1/2}}=2x^{1/2}+5x^{-1/2}\)

Then, you don't need to use the quotient rule any more. However, it looks like your answer is correct. Then, you could simplify it further -

\(\displaystyle x^{-3/2}(x-\frac{5}{2})=x^{-3/2}x-\frac{5}{2}x^{-3/2}=...\)

For the second, it looks to me that your answer is correct.

Then you could simplify it - eg, \(\displaystyle (\sqrt{s}-1)(1)=\sqrt{s}-1\), \(\displaystyle s(\frac{1}{2\sqrt{s}})=\frac{\sqrt{s}}{2}\), etc etc

 

[mmm4444bot]

… I apologize for size errors …

If you use Microsoft Windows (and, my condolences, if you do), then I can tell you how to crop things down to size.

I could have also removed the cursor from your image, in the process.

[attachment=0:29yp5zsv]Cropped.JPG[/attachment:29yp5zsv]