Oct 7, 2015 · Think about dx dx d x d x as d dx(x) d d x (x) which means the derivative of the function x x (taking x x to be the variable--from the denominator of the fraction). Whereas dx(t) dx d x (t) d x …

dx d x appears in differential equations, such us derivatives and integrals. For example, a function f(x) f (x) its first derivative is d dxf(x) d d x f (x) and its integral ∫ f(x)dx ∫ f (x) d x. But I don't really …

The " dx d x " lets people think informally that you're multiplying a height, f(x) f (x), by an "infinitesimal width", dx d x, and then taking an infinite sum.

If f(x) f (x) is in meters per second and dx d x is in seconds, then f(x)dx f (x) d x is in meters, and so is the integral. These things should be dimensionally correct, and are not so without the " dx d x ". …

May 2, 2015 · dy dx =limh→0 f(x + h) − f(x) h. d y d x = lim h → 0 f (x + h) f (x) h and this is is (again) called the derivative of y y or the derivative of f f. Note that it again is a function of x x in this case. …

Sep 9, 2020 · But then others told me that "dx" is part of what's being integrated, and they started saying that we're led to believe that its just a delimiter in early courses because it'd be impossible for …

These identities for dx d x and dx d x are sometimes called the "sophomore's dream". Look that up on Wikipedia.

The dx in the integral is a representation of the fact that the integral is obtained as an area, so multiplying the "average" of the function value at each point by an infinitesimal interval.

What if we want to look at the change of the change? Well, notationally we write d2y dx2 = d dx(dy dx) d 2 y d x 2 = d d x (d y d x) In the previous notation, this would be f′′(x) f ″ (x) and we just 'assume' we …

May 5, 2022 · I've been taught about dy/dx d y / d x and how it can be split into dy dx = d dxy d y d x = d d x y. I'm confused as to why this happens. Don't dy d y and dx d x both refer to infinitely small …