Derivative issue

[Loki123]

So I am confused. For both 1 and 2 my professor says "now we take derivative", however, one includes d one doesn't. Can someone explain the difference, what it means etc??

 

[BigBeachBanana]

The instruction needs to tell you to take the derivative, but with respect to what variable?
In (1), since there is only x, we can assume that it's respect to x.
In (2), you have 3 "unknowns", namely x,t and d. What are you differentiating with respect to?

 

[Steven G]

Your professor, if in fact said what you said, is wrong.
In the first example you found the derivative while in the 2nd example you found the differential.

 

[Steven G]

The instruction needs to tell you to take the derivative, but with respect to what variable?
In (1), since there is only x, we can assume that it's respect to x.
In (2), you have 3 "unknowns", namely x,t and d. What are you differentiating with respect to?

Although I do not support the notation of /d, it means to take the derivative of both sides.

 

[BigBeachBanana]

Although I do not support the notation of /d, it means to take the derivative of both sides.

That's a new one to me and I do not support it either! I was thinking division. That cleared up the OP.

 

[topsquark]

Although I do not support the notation of /d, it means to take the derivative of both sides.

Icky notation!

-Dan

 

[Dr.Peterson]

Although I do not support the notation of /d, it means to take the derivative of both sides.

Can you show documentation of this? I've never heard of such a notation, and it's certainly unclear.

I'd like to see the entire context in which this was presented. I'm guessing it's just something informal used at the board while talking, and not a written notation.

 

[Steven G]

I've seen a number of students on this forum write 2x=7/2 where the /2 was their notation to divide both sides (of 2x=7) by 2

 

[Steven G]

Can you show documentation of this? I've never heard of such a notation, and it's certainly unclear.

I'd like to see the entire context in which this was presented. I'm guessing it's just something informal used at the board while talking, and not a written notation.

We have all seen this before on this forum. I am not going to spend a lot of time looking for an example but will try for a few minutes.

 

[Loki123]

Can you show documentation of this? I've never heard of such a notation, and it's certainly unclear.

I'd like to see the entire context in which this was presented. I'm guessing it's just something informal used at the board while talking, and not a written notation.

Yes, the only times I have seen it is when we write on the board, however, we write it constantly like that.

 

[BigBeachBanana]

Yes, the only times I have seen it is when we write on the board, however, we write it constantly like that.

Did that clear up your confusion about the question?

 

[Loki123]

Did that clear up your confusion about the question?

i think so. But could you tell me what's the difference between differential and derivative?

 

[Steven G]

Let y = (1+x^2)
Then dy/dx = 2x
So dy = 2xdx.
You can think of multiply dy/dx=2x by dx to get dy = 2xdx

 

[Steven G]

i think so. But could you tell me what's the difference between differential and derivative?

I am not going to get into the definition of what a differential is but you mostly use it for integrals. Can you tell us exactly what you are using differentials for?

 

[Loki123]

I am not going to get into the definition of what a differential is but you mostly use it for integrals. Can you tell us exactly what you are using differentials for?

Up until now I didn't know the difference, but from what I can see, we do use it for integrals only.

 

[BigBeachBanana]

i think so. But could you tell me what's the difference between differential and derivative?

Let [imath]\triangle x[/imath] be the change in x, then [imath]\triangle y = f(x+\triangle x)-f(x)[/imath] is the change in y corresponding to how x change. Differentials have practical applications in estimating the max/min potential errors in measurements like volume, area, length, etc... Also, separation of variables to solve differential equations (integration as Steve mentioned).

 

[Shiloh]

The differential, \(\displaystyle \frac{df}{dx}\), is NOT a fraction. It is defined as a limit of fractions: \(\displaystyle \frac{df}{dx}= \lim_{\Dellta x\to 0}\ frac{\Delta y}{\Delta x}\), But it turna out that the derivative can be treat like a fraction. To formalize that we define the "differentials", dx, purely symbolic, and dy, defined as f'(x)dx so that \(\displaystyle \frac{dy}{dx}= f'(x)\) is a fraction.