dy2x

dy2x is not a standard mathematical symbol. In many plain-text writings it appears when someone omits formatting that clarifies the meaning, such as writing dy/dx and getting dy2x, or it may be used to indicate the derivative of y with respect to x when someone intends d(y^2)/dx. Because the string is ambiguous, its meaning depends on context.

If dy2x is intended to mean dy/dx, it denotes the derivative of y with respect to x. This is the instantaneous rate of change of y as x changes, and it is often written as dy/dx or symbolized as y′(x) in calculus.

If dy2x is intended to denote the derivative of y squared with respect to x, it is d(y^2)/dx. By the chain rule, this equals 2 y dy/dx, assuming y is a differentiable function of x. For example, if y = x^2, then dy/dx = 2x and d(y^2)/dx = d(x^4)/dx = 4x^3.

To avoid confusion, standard notation is preferred: use dy/dx for the first derivative and d(y^2)/dx for the derivative of the square of a function. Some texts also write dy^2/dx as shorthand, but this can be ambiguous since it may be read as the derivative of a quantity named y^2 rather than the derivative of y squared with respect to x.

In summary, dy2x is an ambiguous string whose intended meaning should be clarified by context, with the standard interpretations being either dy/dx or d(y^2)/dx. See also dy/dx, derivative, chain rule, and differential notation.