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 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 …

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 " …

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 …

I am working on trying to solve this problem: Prove: $\\int \\sin^n{x} \\ dx = -\\frac{1}{n} \\cos{x} \\cdot \\sin^{n - 1}{x} + \\frac{n - 1}{n} \\int \\sin^{n - 2}{x ...

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

Here, (dx)2 means dx ∧ dx, and the fact that it vanishes comes from the fact that the exterior algebra is anti-commutative. In other words, formally we have d2x = 0 and (dx)2 = 0 but for …

Jan 9, 2015 · 8 dx d x is really an enigma in calculus and differential equations. Leibniz treated it as an “infinitesimal”—a number smaller than any positive number but larger than 0 0. In …

Here, δn =xn −xn−1 δ n = x n x n 1 is providing some measure of how important the bit of space between xn−1,xn x n 1, x n is in computing the integral. The dx d x is what keeps track of that …