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Homework Statement
x2+y2=1
I want to differentiate this equation. I know that the answer is 2x+2y*y'=0.
Homework Equations
The chain rule.
The Attempt at a Solution
I don't understand how you get 2y*y' from y2. Shouldn't it just be 2x+2y=0?
No dy^2/dy=2y.but I see how its 2y*y' because its dy2/dy
What Cyosis wrote in post 8 is the Chain Rule, using Newton's notation. There is no composition rule, althought the Chain Rule is used for finding the derivative of a function composition. In post 2 Cyosis used a different form of the chain rule, that uses Leibniz notiation.Yes, I have seen this. The composition Rule. I thought that exp meant example. What function is it. And for example sin(t)10=9*cos(t) right?
You differentiate y^2 with respect to x, not y! That's where the chain rule comes into play, it really is [itex]y(x)^2[/itex]. As for just explaining it, I am trying but just giving you the result won't do you any good.But I still don't get it. This isn't a homework question. You guy can just explain it to me. I need to learn this to be able to continue with my study of calculus. I have tried but I fail to see where the composition part comes in. All I have is y2.
But the trouble is, y is a function of x, and you want the derivative with respect to x. If you were differentiating with respect to y, it would be easy -- d/dy(y2) = 2y and you're done.But I still don't get it. This isn't a homework question. You guy can just explain it to me. I need to learn this to be able to continue with my study of calculus. I have tried but I fail to see where the composition part comes in. All I have is y2.