- #1

- 831

- 37

## Main Question or Discussion Point

Suppose:

- that I have a function ##g(t)## such that ##g(t) = \frac{dy}{dt} ##;

- that ##y = y(x)## and ##x = x(t)##;

- that I take the derivative of ##g## with respect to ##y##.

One one hand this is ##\frac{dg}{dy} = \frac{dg}{dx}\frac{dx}{dy} = \frac{d^2 y}{dxdt}\frac{dx}{dy}##. On the other hand, if I operate right into ##g = \frac{dy}{dt}## with ##d/dy##, it is ##(d/dy)(dy/dt) = (d/dt)(dy/dy) = 0##. Where is my mistake?

- that I have a function ##g(t)## such that ##g(t) = \frac{dy}{dt} ##;

- that ##y = y(x)## and ##x = x(t)##;

- that I take the derivative of ##g## with respect to ##y##.

One one hand this is ##\frac{dg}{dy} = \frac{dg}{dx}\frac{dx}{dy} = \frac{d^2 y}{dxdt}\frac{dx}{dy}##. On the other hand, if I operate right into ##g = \frac{dy}{dt}## with ##d/dy##, it is ##(d/dy)(dy/dt) = (d/dt)(dy/dy) = 0##. Where is my mistake?