# Chain Rule C4

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#1
I know that I can use the formula dy/dx=dy/du x du/dx but in need to apply the exact chain rule proof to answer the question below.

x^2+y^2=1
0
4 years ago
#2
that would become 2x + 2y(dy/dx)=0

let me explain
you differentiate the x squared normally. then you differentiate the y^2 and get 2y but by the chain rule you multiply it times the derivative of y its self which is dy/dx. The one on the right hand side becomes 0 normally. You could also rearrange to get y in terms of x which you might find easier.
y=(1-x^2)^(1/2) and then use the chain rule
2
4 years ago
#3
Listen its not that difficult! Just use the rule , "if I'm differentiating y then ill just multiply it by y' (or dy/dx if you prefer that)" So for your question it'll become 2x+2y(y' = 0 simply rearrange the equation and you'll get y' = -x/y
2
#4
(Original post by Heisenberg97)
that would become 2x + 2y(dy/dx)=0

let me explain
you differentiate the x squared normally. then you differentiate the y^2 and get 2y but by the chain rule you multiply it times the derivative of y its self which is dy/dx. The one on the right hand side becomes 0 normally. You could also rearrange to get y in terms of x which you might find easier.
y=(1-x^2)^(1/2) and then use the chain rule
Ok i understand that now but i have been asked to lay out the answer using the long proof of the chain rule, is that possible?
0
4 years ago
#5
(Original post by Rea15)
Ok i understand that now but i have been asked to lay out the answer using the long proof of the chain rule, is that possible?
I don't know. At what level are they asking you this? I am only studying A2 further maths atm so if you're at uni I don't think I can help. 0
4 years ago
#6
(Original post by Rea15)
Ok i understand that now but i have been asked to lay out the answer using the long proof of the chain rule, is that possible?
Actually sorry I just read the title of the thread and saw that it says C4 ahah. I don't think (I haven't finished c4 yet so idk and I'm doing edexcel) you are expected to use the long proof of the chain rule at A2 Maths level.
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#7
Yea in school doing c4 module with ccea, teacher just asked could we complete it using the long proof have looked online but can see nothing thanks for our help though
0
4 years ago
#8
(Original post by Rea15)
Ok i understand that now but i have been asked to lay out the answer using the long proof of the chain rule, is that possible?
What have you been asked exactly?
I'm not sure what you mean by long. Can you assume relevant limit laws?
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#9
(Original post by morgan8002)
What have you been asked exactly?
I'm not sure what you mean by long. Can you assume relevant limit laws?
We were just asked to analyse the proof i have attached and using that proof sub in values of the question so that the example uses the proof provided :/
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4 years ago
#10
(Original post by Rea15)
We were just asked to analyse the proof i have attached and using that proof sub in values of the question so that the example uses the proof provided :/
Set u = y, f(y) = y^2. Work through the steps.
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