Understanding Leibniz notation

[T.Vengeance]

I've searched everywhere online and still can't understand it. So I thought I'd give LTT a try. 

 

So if I have a function y = x then the derivative is explained as what is the change in y with an infinitesimally small change in x. In leibniz notation that'd be dy/dx. But I can't understand how to comprehend dx/dx. Or dx²/dx. How is it that you can find the change in x² with an infinitesimally small change in the same x? 

 

(This question comes from me reading about implicit differentiation.)

[Vitalius]

I've searched everywhere online and still can't understand it. So I thought I'd give LTT a try. 

 

So if I have a function y = x then the derivative is explained as what is the change in y with an infinitesimally small change in x. In leibniz notation that'd be dy/dx. But I can't understand how to comprehend dx/dx. Or dx²/dx. How is it that you can find the change in x² with an infinitesimally small change in the same x? 

 

(This question comes from me reading about implicit differentiation.)

I have taken 3 calculus classes.

I still don't get it.

[T.Vengeance]

I have taken 3 calculus classes.

I still don't get it.

I wish we could just use the f prime notation . But I know that apparently Leibniz notation is much more useful...

[Vitalius]

I wish we could just use the f prime notation . But I know that apparently Leibniz notation is much more useful...

"apparently"

[helping]

It's actually quite straight forward
 
you have to consider chain rule and as you'll find it WILL be necessary to when finding rates of and implicit differentiation. It'll seem strange at first but don't worry too much, it'll be second nature by soon enough.
 
When you start U subs it might become more clear. 
 
fx prime and double prime etc notation is only really useful for something like taylor series when you need to keep track of all dem primes. 
 
what exactly are you stuck on? And I have no idea what dx^2/dx means
 

So if I have a function y = x then the derivative is explained as what is the change in y with an infinitesimally small change in x. In leibniz notation that'd be dy/dx. But I can't understand how to comprehend dx/dx. Or dx²/dx. How is it that you can find the change in x² with an infinitesimally small change in the same x? 

 

d means nothing but derivative, and dy/dx means the derivative of X with respect to Y, that is, the dy = xdx 

 

You're over thinking or over complicating it. When you have y = x^2, derivative function is dy/dx = 2xdx, where dx is the derivative of X from the application of the chain rule.

 

If you had y = sin(x), you would have the derivative function  dy/dx = cos(x)dx (chain rule)

if you had y = sin(2x), you would have dy/dx = cos(2x)*(2) chain rule

etc

 

In situations where dx/dx or dy/dy would be appropriate, you don't have to bother writing it because you can treat that as a 1. 

 

just roll with it, once you start doing more integration and subs it'll become more clear. 

[Vitalius]

It's actually quite straight forward

 

you have to consider chain rule and as you'll find it WILL be necessary to when finding rates of and implicit differentiation. It'll seem strange at first but don't worry too much, it'll be second nature by soon enough.

 

When you start U subs it might become more clear. 

 

fx prime and double prime etc notation is only really useful for something like taylor series when you need to keep track of all dem primes. 

 

what exactly are you stuck on?

I know what you are talking about, but I don't know what you are talking about. 

[nicehat]

the rate of change in x with respect to x. So since x = x, dx/dx = 1?

 

so if we try getting the derivative of

  y      =         x^3  +       x

dy/dx = d/dx(x^3) + dx/dx?

 

         = 3x^2 + 1?

 

I have no idea what im talking about, but I think that makes sense.. its been a while. 

[T.Vengeance]

I know what you are talking about, but I don't know what you are talking about. 

-snip-

LOL

 

 

It's actually quite straight forward

 

you have to consider chain rule and as you'll find it WILL be necessary to when finding rates of and implicit differentiation. It'll seem strange at first but don't worry too much, it'll be second nature by soon enough.

 

When you start U subs it might become more clear. 

 

fx prime and double prime etc notation is only really useful for something like taylor series when you need to keep track of all dem primes. 

 

what exactly are you stuck on? And I have no idea what dx^2/dx means 

 

GOT IT (and I feel kinda stupid now).

 

Was reading about implicit differentiation of a unit circle. And I just got a bit confused but now I'm good. I just realized that I could've gone a step further from what I just said. If y = x² then dy/dx is exactly the same as dx²/dx. Just WOOOOW. So now it makes sense why dx²/dx = 2x.