I have a function given implicitly, you know. X and Y on both sides. Then it says, assume y = y(x). That's fine. I should be able to find y'(0), but what about y''(0)? How do you treat the dy/dx parts when taking the second derivative?
Edit: I would also like to follow the tip in the book, that says when I'm after actual values. We can just insert the value instead solving for dy/dx.
Best Answer
If you can use partial derivatives, then you can do the following:
First you find $dy/dx$, say $$\frac{dy}{dx}=g(x,y).$$ Then by chain rule $$\frac{d^2y}{dx^2}=\frac{\partial g}{\partial x}+\frac{\partial g}{\partial y}\frac{dy}{dx}=\frac{\partial g}{\partial x}+\frac{\partial g}{\partial y}g(x,y).$$