anonymous
  • anonymous
Cal 1: Find the derivative:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
|dw:1377664443864:dw|
anonymous
  • anonymous
Would i start by writing it as: (5-7x^1/2)^1/2?
Luigi0210
  • Luigi0210
Yup

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anonymous
  • anonymous
Then after that, I got this: 1/2(5-7x^1/2)(-7/2x^-1/2)
anonymous
  • anonymous
Well wait. I got 1/2 (5-7x^1/2)^-1/2(-7/2x^-1/2)
Luigi0210
  • Luigi0210
Wouldn't this be triple chain rule?
anonymous
  • anonymous
I think. Did i mess up somewhere or not finish the problem? Im a little stuck.
Psymon
  • Psymon
Without the equation editor its hard to make out all the lines of numbers xD
anonymous
  • anonymous
Ok, give me some time to write it out in the editor
Psymon
  • Psymon
Looks like you got the right idea, just can't tell for certain. Ill post what you should have :P
anonymous
  • anonymous
Ok that will work!
Luigi0210
  • Luigi0210
Okay.. Psymon's gonna kick me out now.. see you, good luck.
anonymous
  • anonymous
You are both welcome to stay :) haha
anonymous
  • anonymous
Any explanations will be appreciated.
Psymon
  • Psymon
\[\frac{ 1 }{ 2 }(5-\sqrt{7x})^{-\frac{ 1 }{ 2 }} (-\frac{ 1 }{ 2 })(7x)^{-\frac{ 1 }{ 2 }}(7)\] im not kicking you out @_@
anonymous
  • anonymous
Ok so how did you originally re-write the problem?
anonymous
  • anonymous
|dw:1377665401944:dw| Is that how you should rewrite it?
Psymon
  • Psymon
Well, I never really "rewrote" it. I kinda justdid chain chain chain o.o
anonymous
  • anonymous
I usually try to get rid of the roots before solving the problem. Would that ^^^ be correct? I cannont get the answer you are getting
anonymous
  • anonymous
|dw:1377665908253:dw| This is what im doing.. I feel like it is incorrect.
Psymon
  • Psymon
Alright, lets look at this in layers as best as we can. So we originally have: \[\sqrt{5-\sqrt{7x}} \]I like to say that this is 3 layers here. Or 3 inner functions if you prefer. The chain rule is where we take the derivative of each layer and then multiply those derivatives together. So this is how I would define the layers. I like to leave blanks so I dont confuse myself with so many numbers on my paper. So these our are 3 layers: \[\sqrt{-----}\] \[5-\sqrt{--}\] \[7x \] So we have 3 layers and we need 3 derivatives. So starting with the first one, pretend its empty. How would I take the derivative of the square root of something?
anonymous
  • anonymous
I tend to re write it as a power. soo \[1/2x^-1/2\]
anonymous
  • anonymous
To take the derivative of a square root, turn it into a power. Then bring 1/2 in front and subtract the exponent from 1.
Luigi0210
  • Luigi0210
|dw:1377667123161:dw| My educated try
Luigi0210
  • Luigi0210
@helloimjared
stamp
  • stamp
|dw:1377667145358:dw|
Psymon
  • Psymon
Sorry, im alive. And yeah, I rewrite it as apower myself usually. But yes, the first portion you have is \[\frac{ 1 }{ 2 }(--)^{-\frac{ 1 }{ 2 }}\] Oh, you tried it xD Looks like you only missed a sign I think from the looks of it.
Psymon
  • Psymon
\[\frac{ 1 }{ 2 }(--)^{-\frac{ 1 }{ 2 }}*-\frac{ 1 }{ 2 }(--)^{-\frac{ 1 }{ 2 }}*7\] Now just fil in the blanks and simplify. I believe you had the same thing with a different sign.
anonymous
  • anonymous
The way Luigi solved it is how i intend to solve it myself. I see where I messed up though. I just didnt take in the 3rd chain (\[\sqrt{7}\])
Psymon
  • Psymon
Well, my answer is the same as stamps EXCEPT I havea 4 in the denominator.
anonymous
  • anonymous
When I originally solved it, I combined 2 parts into 1 step.
stamp
  • stamp
Wolfram says there should be a 4. I want to do this over bcuz I am not confident in my rigor
Luigi0210
  • Luigi0210
I got a 4, yes >.<
Psymon
  • Psymon
Yeah, I ended up with a 4. I thought it was clear to see how I got the 4. If what I did above makes sense.
anonymous
  • anonymous
The 4 just comes from the simplifying part right?
Luigi0210
  • Luigi0210
Yup
Psymon
  • Psymon
Well because 2 of my 3 layers hadasquare root, meaning a 1/2 power was brought down twice, accounting for the 4.
anonymous
  • anonymous
Ok great. Thank you everyone so much. I understand it! I was almost right to start off with.. I just combined 2 steps :C
Psymon
  • Psymon
Cool, cool ^_^ Yeah, these are be careful problems. Once you can do a problem like this, you can do pretty much any problem given you are careful xD

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