Review the different common ways of writing derivatives.
Log in Tenacious 8 years agoPosted 8 years ago. Direct link to Tenacious's post “Why haven't I seen Newton...” Why haven't I seen Newton's method - the 'dot' - in any of my college calc courses? • (124 votes) Christopher Clements 8 years agoPosted 8 years ago. Direct link to Christopher Clements's post “I have used dot notation ...” I have used dot notation to a great extent in classical mechanics to note first(dot) and Second(double dot) derivatives...more out of laziness than anything else. "Pure" mathematicians rarely, if ever, use this notation in my experience. Many are in fact rather critical of this notation in all cases save 4th or greater derivatives where even the theorists get lazy :) (53 votes) brycepietila 8 years agoPosted 8 years ago. Direct link to brycepietila's post “Just curious. Why is dy/d...” Just curious. Why is dy/dx a correct way to notate the derivative of cosine or any specific function for that matter? If I only wrote dy/dx on a piece of paper and asked somebody to differentiate, then I would hope they would not say that the derivative is negative sine • (57 votes) Christopher Clements 8 years agoPosted 8 years ago. Direct link to Christopher Clements's post “Alex, you are 100% correc...” Alex, you are 100% correct. If the function is not know dy/dx simply means some derivative y in relation to x (31 votes) octmacs 8 years agoPosted 8 years ago. Direct link to octmacs's post “Leibniz's notation made m...” Leibniz's notation made me confused a lot when I first met it in calculus integral. I always thought it is kind of y/x rather than y', for I had already seen dx in integral a long time ago before I seen dy/dx. It seems that this notation is far different from the other two, for does it have other functions when written differently? • (20 votes) HMankodiya 7 years agoPosted 7 years ago. Direct link to HMankodiya's post “yup "d" just small change...” yup "d" just small change ......very small we can say that """d""" is just small DELTA (6 votes) KHJ 8 years agoPosted 8 years ago. Direct link to KHJ's post “I heard that newton's not...” I heard that newton's notations are very complex as it uses many notations like dots or hats in random. Is that true? • (13 votes) Scottyboy1 7 years agoPosted 7 years ago. Direct link to Scottyboy1's post “It's not that it's more c...” It's not that it's more complex, it's just that he was a physics and math wiz. His dots can add up quickly in mathematics because you might be taking the 10th (for example) derivite of some quantity. That would look like this: . No thanks! Lol In physics you are just looking for the first derivative (velocity) and the second derivate (acceleration).........and once in a while (like almost never) you will need the third derivative, which is (jerk). So the most dots you would get are 3. When you think about it, d/dx is a lot to write down when you can just write (dot). But too many dots would make each equation too cumbersome to write. (46 votes) Harsh Chauhan 7 years agoPosted 7 years ago. Direct link to Harsh Chauhan's post “What is difference betwee...” What is difference between derivative and differentiation? • (13 votes) Aaron Priester 7 years agoPosted 7 years ago. Direct link to Aaron Priester's post “Differentiation is the pr...” Differentiation is the process of finding a derivative of a function, I think you could say. (37 votes) Clara Wessels 4 years agoPosted 4 years ago. Direct link to Clara Wessels's post “In Leibniz notation, when...” In Leibniz notation, when would you use dy/dx and when would you use d/dx? Or are these two notations interchangeable? Am I correct to say that when the function is given in the form f(x)=..., you would write the derivative as d/dx(fx), and when given as y=..., you would write it as dy/dx(y)? • (19 votes) Anuvesh Kumar a year agoPosted a year ago. Direct link to Anuvesh Kumar's post “You can think of Leibniz ...” You can think of Leibniz notation as just d/dx of something which means it's the derivative of something w.r.t. x. 1. If that something is just an expression you can write d(expression)/dx. so if expression is x^2 then it's derivative is represented as d(x^2)/dx. 2. If we decide to use the functional notation, viz. f(x) then derivative is represented as d f(x)/dx. Note that 'f(x)' is not a variable, all it says is that f is a function of x, which is given by some You can imagine if the expression is large, it'll be cumbersome to write d(expression)/dx. So this notation as well as the next is useful in that context. 3. If instead of using functional notation we decide to use the notation of dependent variable, as in the value of the variable depends on something, where the something can be either an expression or a function. then dy/dx then represents the derivative of dependent variable w.r.t x. TO SUMMARIZE: dependent variable = function of x = expression OR y = f(x) = x^2 then, dy/dx = d(f(x))/dx = d(x^2)/dx (8 votes) User 5939293 a year agoPosted a year ago. Direct link to User 5939293's post “Is this correct for y=cos...” Is this correct for y=cos(x): • (12 votes) Venkata a year agoPosted a year ago. Direct link to Venkata's post “Yes, that's correct.” Yes, that's correct. (7 votes) lj08197 2 years agoPosted 2 years ago. Direct link to lj08197's post “I'm middle school i dont ...” I'm middle school i dont get the difference between d/dy and dx/dy and dy/dx etc. • (6 votes) Iron Programming 2 years agoPosted 2 years ago. Direct link to Iron Programming's post “Howdy lj08197,What you ...” Howdy lj08197, What you are asking about is called the Leibniz notation for derivatives. With this notation, d/dx is considered the derivative operator. So if we say d/dx[f(x)] we would be taking the derivative of f(x). The result of such a derivative operation would be a derivative. In our case, we took the derivative of a function (f(x), which can be thought as the dependent variable, y), with respect to x. We write that as dy/dx. Let's look at some examples. If you are comparing this notation to other notation, such as f' (pronounced f prime), then dy/dx would be the equivalent of f'(x), the derivative of f(x). Hope this helps! (19 votes) bhannon039 7 years agoPosted 7 years ago. Direct link to bhannon039's post “In my physics book, it ap...” In my physics book, it appears there is some sort of algebra involved using the derivative notation itself. For example, with the work-kinetic energy theorem there is the following result: dv/dt = (dv/dx)*(dx/dt) = (dv/dx)*v It wasn't explained in the book and I am trying to find where I can figure out where this came from. • (7 votes) andrewp18 7 years agoPosted 7 years ago. Direct link to andrewp18's post “That is the chain rule in...” That is the chain rule in action! (15 votes) lupinx2 3 years agoPosted 3 years ago. Direct link to lupinx2's post “Why isd-- g(x)dxa co...” Why is • (3 votes) KLaudano 3 years agoPosted 3 years ago. Direct link to KLaudano's post “d/dx is an operation that...” d/dx is an operation that means "take the derivative with respect to x" whereas dy/dx indicates that "the derivative of y was taken with respect to x". (13 votes)Want to join the conversation?
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y
so y = x^2 or y = f(x)
d cos(x) / dx
(1.) d/dx[f(x)] = dy/dx (we took the derivative of f(x) with respect to x)
(2.) d/dt[f(t)] = dy/dt (we took the derivative of f(t) with respect to t)
(3.) d/dt[f(x)] = Not Application (N/A). There is no variable t in this function!
(4.) d/dx[2x + 3] = Take the derivative of the expression "2x + 3" with respect to x. You will learn how to do this later.
[𝑓(𝑔(𝑥))]' = 𝑓'(𝑔(𝑥))𝑔'(𝑥)
In Leibniz notation this is:
(𝑑𝑓)/(𝑑𝑥) = [(𝑑𝑓)/(𝑑𝑔)] • [(𝑑𝑔)/(𝑑𝑥)]
In your case, (𝑑𝑥)/(𝑑𝑡) is velocity 𝐯 (change in position per change in time). I suggest you watch the videos on Chain Rule. Comment if you have questions!
d
-- g(x)
dx
a correct notation for the derivative of g(x)? shouldn't it be dy on top?
