Thread: Implicit Differation and Chain Rule

First, I really need help with implicit differentiation. I tried reading in my book, but they use very basic problems and I did not find it helpful.
The problem I need help with is:

x^2 + xy - y^2 = 4 Solver for y'
I can not get the correct answer. I got (2x)/(x-2y)=y' (This is incorrect).

Next I need help with the chain rule. I understand how to do this, but I am having problems with one question. The question is:

Sqrt (2x)/(x^2+1.8)) <- For this problem, everything is under the radical.

Thank you!!!

Hello,

Originally Posted by PensFan10

First, I really need help with implicit differentiation. I tried reading in my book, but they use very basic problems and I did not find it helpful.
The problem I need help with is:

x^2 + xy - y^2 = 4 Solver for y'
I can not get the correct answer. I got (2x)/(x-2y)=y' (This is incorrect).

Your only mistake (that I found by analysing your answer, so sorry if you did it right..) is that the derivative of xy has to be taken with the product rule :



As soon as the variable intervenes in x, y, z, t, or whatever, you have to consider it as a function, not like a variable, so you're likely to use the product, quotient or chain rule =)

Next I need help with the chain rule. I understand how to do this, but I am having problems with one question. The question is:

Sqrt (2x)/(x^2+1.8)) <- For this problem, everything is under the radical.

Thank you!!!

The chain rule says that the derivative is

So calculate with the quotient rule.

Always do things step by step. It's pretty tricky for someone who is not used to differentiating to do it without taking u(x).

That was stupid of me to mess up the xy (product rule). Doh! Thanks for catching that mistake.

Thanks a lot for the help!!!

So I solved chain rule problem out and got an answer of:

(1)/(XSqrt(2x/x^2+1.8))

Just curious if I did it correct. Once again, Thanks!

Originally Posted by PensFan10

So I solved chain rule problem out and got an answer of:

(1)/(XSqrt(2x/x^2+1.8))

Just curious if I did it correct. Once again, Thanks!

Hmm; that's a weird one.

What do you find as the derivative ?
Because I doubt it is /:

Can you show your working so that I can tell you where the mistake(s) is(are) ?

Okay, I see how I messed up.
Heres my current solution attempt :P

For u'(x) I have this:

2x/(x^2+1.8)

Quotient rule says: gf'-fg'/g^2

When I plug my info in I got:

(x^2+1.8)(2)-(2x)(2x)/(x^2+1.8)^2
Simplified:
2x^2+3.6-4x^2/(x^2+1.8)^2

=-2x^2+3.6/(x^2+1.8)^2

Now I plug that into u'(x)/(2Sqrt u(x))

I got

-2x^2+3.6
-----------------
(x^2+1.8)^2
------------------
2Sqrt(2x/x^2+1.8)

Might be just me, but I think I did something wrong again.

Originally Posted by PensFan10

Okay, I see how I messed up.
Heres my current solution attempt :P

For u'(x) I have this:

2x/(x^2+1.8)

Quotient rule says: gf'-fg'/g^2

When I plug my info in I got:

(x^2+1.8)(2)-(2x)(2x)/(x^2+1.8)^2
Simplified:
2x^2+3.6-4x^2/(x^2+1.8)^2

=-2x^2+3.6/(x^2+1.8)^2

Now I plug that into u'(x)/(2Sqrt u(x))

I got

-2x^2+3.6
-----------------
(x^2+1.8)^2
------------------
2Sqrt(2x/x^2+1.8)

Might be just me, but I think I did something wrong again.

Ignoring the missing parentheses, this is correct

Note that you can write and simplify the fraction by 2

The solution is :



-----------------------------
do you understand the red part ?

, and
-----------------------------

Simplifying the powers by this rule : , we get :



Now it depends on how you want to display the result

Yes the red part was you moving the denominator to the numerator. Thanks so much and sorry about the missing parentheses. If I knew you, I would buy you a drink

Originally Posted by PensFan10

Yes the red part was you moving the denominator to the numerator. Thanks so much and sorry about the missing parentheses. If I knew you, I would buy you a drink

Great, I was being thirsty !

Originally Posted by PensFan10

First, I really need help with implicit differentiation. I tried reading in my book, but they use very basic problems and I did not find it helpful.
The problem I need help with is:

x^2 + xy - y^2 = 4 Solver for y'
I can not get the correct answer. I got (2x)/(x-2y)=y' (This is incorrect).

Next I need help with the chain rule. I understand how to do this, but I am having problems with one question. The question is:

Sqrt (2x)/(x^2+1.8)) <- For this problem, everything is under the radical.

Thank you!!!

Alternatively for the second one, Let



So differentiating we get



and now remembering that y is our original equation we see



EDIT:

Same concept, just a little less messy to write

i kind of see what you did. I understand squaring both sides and then taking the derivative. I got lost after you simplified.

how did you go from 2(x^2+1.8)-(2x)(2x) to -2(x^2-1.8) (i left out the denominator to be less confusing)

Second, is that actually supposed to be a 4.8 in the numerator in your final answer or is it a typo. *EDIT* never mind. i see you changed it. now that part makes more sense :P

Originally Posted by PensFan10

i kind of see what you did. I understand squaring both sides and then taking the derivative. I got lost after you simplified.

how did you go from 2(x^2+1.8)-(2x)(2x) to -2(x^2-1.8) (i left out the denominator to be less confusing)

Second, is that actually supposed to be a 4.8 in the numerator in your final answer or is it a typo.

That is a typo that I fixed, and secondly

Ha. Not sure how I didn't see that Thanks. I really like that way.