Cal 1: Find the derivative:

- anonymous

Cal 1: Find the derivative:

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- schrodinger

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- anonymous

|dw:1377664443864:dw|

- anonymous

Would i start by writing it as: (5-7x^1/2)^1/2?

- Luigi0210

Yup

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

Then after that, I got this: 1/2(5-7x^1/2)(-7/2x^-1/2)

- anonymous

Well wait. I got 1/2 (5-7x^1/2)^-1/2(-7/2x^-1/2)

- Luigi0210

Wouldn't this be triple chain rule?

- anonymous

I think. Did i mess up somewhere or not finish the problem? Im a little stuck.

- Psymon

Without the equation editor its hard to make out all the lines of numbers xD

- anonymous

Ok, give me some time to write it out in the editor

- Psymon

Looks like you got the right idea, just can't tell for certain. Ill post what you should have :P

- anonymous

Ok that will work!

- Luigi0210

Okay.. Psymon's gonna kick me out now.. see you, good luck.

- anonymous

You are both welcome to stay :) haha

- anonymous

Any explanations will be appreciated.

- Psymon

\[\frac{ 1 }{ 2 }(5-\sqrt{7x})^{-\frac{ 1 }{ 2 }} (-\frac{ 1 }{ 2 })(7x)^{-\frac{ 1 }{ 2 }}(7)\]
im not kicking you out @_@

- anonymous

Ok so how did you originally re-write the problem?

- anonymous

|dw:1377665401944:dw|
Is that how you should rewrite it?

- Psymon

Well, I never really "rewrote" it. I kinda justdid chain chain chain o.o

- 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

|dw:1377665908253:dw|
This is what im doing.. I feel like it is incorrect.

- 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

I tend to re write it as a power. soo \[1/2x^-1/2\]

- 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

|dw:1377667123161:dw|
My educated try

- Luigi0210

@helloimjared

- stamp

|dw:1377667145358:dw|

- 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

\[\frac{ 1 }{ 2 }(--)^{-\frac{ 1 }{ 2 }}*-\frac{ 1 }{ 2 }(--)^{-\frac{ 1 }{ 2 }}*7\] Now just fil in the blanks and simplify. I believe you had the same thing with a different sign.

- anonymous

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

Well, my answer is the same as stamps EXCEPT I havea 4 in the denominator.

- anonymous

When I originally solved it, I combined 2 parts into 1 step.

- stamp

Wolfram says there should be a 4. I want to do this over bcuz I am not confident in my rigor

- Luigi0210

I got a 4, yes >.<

- 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

The 4 just comes from the simplifying part right?

- Luigi0210

Yup

- Psymon

Well because 2 of my 3 layers hadasquare root, meaning a 1/2 power was brought down twice, accounting for the 4.

- 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

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.