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What is the difference between $dy$ and $Δy$ and why is $dx$ is same as . . . For examples, this dy d y as δy δ y and dx d x as δx δ x notation is used in videos like the ones mentioned in a comment by the OP Yashasv Prajapati: blackpenredpen 's “ delta y vs dy (differential) ” and The Math Sorcerer 's “ How to Compute Delta y and the Differential dy ”
In differential calculus, why is dy dx written as d dx ( y)? In differential calculus, We know that dy dx is the ratio between the change in y and the change in x In other words, the rate of change in y with respect to x Then, why is dy dx written as d dx
dy dx . . . what are we really saying? What is dx? [duplicate] Additional Note: When given an equation like: dy dx = 2x d y d x = 2 x You could re-write it as: dy = 2xdx d y = 2 x d x If you integrate the left hand side with respect to y y and the right hand side with respect to x x, you get y =x2 + c y = x 2 + c In this process one may be lead to think that dx d x is a variable
Why is the 2nd derivative written as - Mathematics Stack Exchange Here, the numerator represents d(dy) d (d y), or just the "operation" d() d () being performed on y twice, thus we can write it as d2y d 2 y In constrast, the denominator represents squaring dx d x Since dx d x is one "variable", we can remove the parentheses, resulting in the term dx2 d x 2
derivatives - Proof of dy=f’ (x)dx - Mathematics Stack Exchange It's merely a symbolic notation, used to simplify some expressions If you will, just take dy = f′(x)dx d y = f ′ (x) d x as the definition of the symbols dy, dx d y, d x Note that these (at least for now) are no real mathematical objects (in the sense that they are rigorously defined), and just serve to make some stuff a bit tidier
What exactly are dx and dy in differential equations? In undergraduate differential equations courses, calculations that involve manipulating dx d x and dy d y as independent quantities can always be rephrased easily to avoid doing so (That said, "infinitesimal intuition" should not be thrown out the window For intuition, we can think of dx d x and dy d y as tiny but finite quantities and do calculations with them, obtaining approximate