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) …

A "signed definite integral" for computing work and other "net change" calculations. The value of an expression such as $\int_0^1 x^2\,dx$ comes out the same under all these interpretations, …

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.

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 …

Dec 27, 2013 · Δx Δ x, δx δ x and dx d x are used when talking about slopes and derivatives. But I don't know what the exact difference is between them.

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 " …

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

Here, $ (dx)^2$ means $dx \wedge dx$, and the fact that it vanishes comes from the fact that the exterior algebra is anti-commutative. In other words, formally we have $d^2x=0$ and $ …

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 …

Dec 28, 2025 · Now, he said, let the integrand be $f (4-x^2)$, since $f (k)$ is attained for two different values of $x$, there must be "two corresponding dx for it", say $dx_1$ and $dx_2$.