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What does the dx mean in an integral? [duplicate] 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
calculus - What is the true, formal meaning and reason for the dx . . . Prior to the 1800s, "dx" was considered an "infinitesimal" - a number so close to zero that, for some things, it can be considered actually zero, but wasn't exactly zero In the 1800s, the failure to formalize infinitesimals (and, in my opinion, the growing rise of materialism) led to the belief that infinitesimals were invalid mathematical
What does $\\frac{d^6y}{ dx^6}$ mean? - Mathematics Stack Exchange The symbol " d dx d d x " is used to indicate a single derivative (with respect to x x) We treat repeated application of this operator symbolically as "powers" of the operator (as if it were ordinary multiplication by an ordinary fraction), writing " dn dxn d n d x n " to indicate n n successive applications of " d dx d d x "
calculus - Understanding the syntax for derivatives - dy dx . . . 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 took the derivative with respect to x x since it is the only input variable for f f