I want to differentiate this equation. I know that the answer is 2x+2y*y'=0.
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?
but I see how its 2y*y' because its dy2/dy
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?
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.
It's not "y with respect to x"; it's the derivative of y with respect to x. Once you understand what the symbols mean, the dy/dx notation of Leibniz is much superior, IMO, to the Newton-style notation. For one thing dy/dx is more suggestive of the difference quotient (f(x+h) - f(x))/h or [itex]\Delta y/\Delta x[/itex]. For another, it tells you exactly what the independent variable is; IOW, what the variable with respect to which you're differentiating. As Cyosis pointed out, that information isn't present in u'.The equation for the chain rule is (un)'*u'? Why didn't you say that? It makes since now. The dy/dx notation is confusing. I know that it's y with respect to x but it's not as easy to visualize as u'.
If I am still mistaken I still don't get it. Can you explain it with out y(x) and dy/dx? Just use y' and y2. The video on that site helped but I already knew that. Doing this with trig functions is super easy.