Where am I going wrong?

[ricecrispie]

I now need help with another quotient problem if you're not busy! I'll attach a file with my working and quotient rule

1) Please state the "Quotient Rule".
2) Please demonstrate how you have implemented it.

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[ricecrispie]

Can I pick your brain about 1 more quotient rule question? I've attached my working and will really appreciate any feedback if you aren't too busy

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[ricecrispie]

Hi all! I have another quotient rule question, I couldn't reply on my previous post for some reason but thanks to everyone that responded I got it eventually but now I'm stuck on this question. I've attached my working out, will appreciate any feedback

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[stapel]

Hi all! I have another quotient rule question, I couldn't reply on my previous post for some reason but thanks to everyone that responded I got it eventually but now I'm stuck on this question. I've attached my working out, will appreciate any feedback View attachment 10013

The text in the image is too small and blurry for me to read. Please reply with clarification, using standard web-safe formatting. Thank you!

 

[ricecrispie]

Sorry about that! I wonder why it became so blurry, I'll try type it out as best as I can:

Differentiate:

y = (s - s^1/2) / s^2

I said:

y' = [s^2(1 - 1/2s^-1/2) - (2s)(s - s^1/2)] /s^4

= [s^2 - 1/2s^3/2 - 2s^2 + 2s^3/2] /s^4

= (-s^2 - 3/2s^3/2) / s^4

But the solution given is:

y' = (3 - 2s^1/2) / 2s^5/2

I have no idea how to get to this

The text in the image is too small and blurry for me to read. Please reply with clarification, using standard web-safe formatting. Thank you!

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[Dr.Peterson]

Hi yes I did that and it worked out, thanks for the help! Can I pick your brain about 1 more quotient rule question? I've attached my working and will really appreciate any feedback if you aren't too busyView attachment 10012

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This should be in a separate thread. Its posting was delayed for moderation, but you should now be able to get through more quickly.

The picture apparently was degraded because it was too large. On a computer, you can fix this by displaying it and "snipping" the appropriate piece at screen resolution. I don't know if anyone has a nice workaround for phones, but you'll have to edit the picture somehow.

 

[ricecrispie]

This should be in a separate thread. Its posting was delayed for moderation, but you should now be able to get through more quickly.

The picture apparently was degraded because it was too large. On a computer, you can fix this by displaying it and "snipping" the appropriate piece at screen resolution. I don't know if anyone has a nice workaround for phones, but you'll have to edit the picture somehow.

Thank you I understand now, I'll start new threads for new questions.

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[ricecrispie]

Reply to stapel: quotient problem

Hi, I can't reply yet, thanks to everyone who helped but I really need help with this question, I'm sorry the picture was of poor quality, I tried to type it out as best as I could.

Differentiate:

y = (s - s^1/2) / s^2

I said:

y' = [s^2(1 - 1/2s^-1/2) - (2s)(s - s^1/2)] /s^4

= [s^2 - 1/2s^3/2 - 2s^2 + 2s^3/2] /s^4

= (-s^2 - 3/2s^3/2) / s^4

But the solution given is:

y' = (3 - 2s^1/2) / 2s^5/2

I have no idea how to get to this

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[Dr.Peterson]

Differentiate:

y = (s - s^1/2) / s^2

I said:

y' = [s^2(1 - 1/2s^-1/2) - (2s)(s - s^1/2)] /s^4

= [s^2 - 1/2s^3/2 - 2s^2 + 2s^3/2] /s^4

= (-s^2 - 3/2s^3/2) / s^4

But the solution given is:

y' = (3 - 2s^1/2) / 2s^5/2

I have no idea how to get to this

Thanks for parenthesizing well (mostly). This is pretty clear.

I'll repeat what you did, with some extra braces to identify the exponents, and one little fix:

y = (s - s^{1/2}) / s^2


y' = [s^2(1 - 1/2s^{-1/2}) - (2s)(s - s^{1/2})] /s^4

= [s^2 - 1/2s^{3/2} - 2s^2 + 2s^{3/2}] /s^4

= (-s^2 + 3/2s^{3/2}) / s^4

The sign on that last line is the only actual error. Now you have to factor out the smallest power of s, which is s^{3/2}:

= (3/2s^{3/2} - s^2) / s^4
= (3/2s^{3/2} - s^{1/2}s^{3/2}) / s^4
= (3/2 - s^{1/2})s^{3/2} / s^{8/2}
= (3/2 - s^{1/2})/s^{5/2}

At the end I canceled s^{3/2}, that is, subtracted 3/2 from both exponents.

Now just multiply numerator and denominator by 2 to clear fractions. Don't forget parentheses in the denominator of your final result, which are needed for clarity.

 

[ricecrispie]

Thank you so much ! This helps a lot!

Thanks for parenthesizing well (mostly). This is pretty clear.

I'll repeat what you did, with some extra braces to identify the exponents, and one little fix:

y = (s - s^{1/2}) / s^2


y' = [s^2(1 - 1/2s^{-1/2}) - (2s)(s - s^{1/2})] /s^4

= [s^2 - 1/2s^{3/2} - 2s^2 + 2s^{3/2}] /s^4

= (-s^2 + 3/2s^{3/2}) / s^4

The sign on that last line is the only actual error. Now you have to factor out the smallest power of s, which is s^{3/2}:

= (3/2s^{3/2} - s^2) / s^4
= (3/2s^{3/2} - s^{1/2}s^{3/2}) / s^4
= (3/2 - s^{1/2})s^{3/2} / s^{8/2}
= (3/2 - s^{1/2})/s^{5/2}

At the end I canceled s^{3/2}, that is, subtracted 3/2 from both exponents.

Now just multiply numerator and denominator by 2 to clear fractions. Don't forget parentheses in the denominator of your final result, which are needed for clarity.

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[mmm4444bot]

… I wonder why it became so blurry …

:idea: The reason why you're wondering is because you have not read the forum guidelines. This is the same reason for why you're submitting duplicate posts.

 

[ricecrispie]

Yes sorry about that, completely my mistake, I was stressing about an upcoming maths test and thought it was a waste of time to read the guidelines, I've read them now and I'm really sorry to anyone that got a little confused about my duplicate responses, sorry for the bother

:idea: The reason why you're wondering is because you have not read the forum guidelines. This is the same reason for why you're submitting duplicate posts.

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