There are a number of simple rules which can be used to allow us to differentiate many functions easily. If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the derivative of y (with respect to x) is written dy/dx, pronounced "dee y by dee x" .

What is the difference between D dx and dy dx?

d/dx is differentiating something that isn't necessarily an equation denoted by y. dy/dx is a noun. It is the thing you get after taking the derivative of y. d/dx is used as an operator that means "the derivative of".

What exactly is dy dx?

The symbol dydx. means the derivative of y with respect to x. If y=f(x) is a function of x, then the symbol is defined as dydx=limh→0f(x+h)−f(x)h. and this is is (again) called the derivative of y or the derivative of f. Note that it again is a function of x in this case.