How to differentiate an equation

[GBA13]

Homework Statement

Hi Everyone,

This seems like a very simple question but I' a bit confused.

In maths if I wanted to differentiate y = x^2 then it would just be 2x but I'm not sure about what you would do in physics. If you had the equation C = m/V (Concentration = mass/volume) how can you differenicate that with respect to time or something?

Homework Equations

The Attempt at a Solution

Surely what ever type of differentiation you did (normal, partial etc.) all the parts would just end up being 0 so the differential is zero.

Can someone please set me straight.

Thanks,

 

[mfb]

In maths if I wanted to differentiate y = x^2 then it would just be 2x

If you calculate the derivative with respect to x.

If you had the equation C = m/V (Concentration = mass/volume) how can you differenicate that with respect to time or something?

Do m or V depend on time?
If yes (how?), you have to take this into account. Simple example: m=c*t with some constant t leads to a non-zero time derivative.
If no, they are just constants.

 

[rude man]

Homework Statement

Hi Everyone,

This seems like a very simple question but I' a bit confused.

In maths if I wanted to differentiate y = x^2 then it would just be 2x but I'm not sure about what you would do in physics. If you had the equation C = m/V (Concentration = mass/volume) how can you differenicate that with respect to time or something?

Homework Equations

The Attempt at a Solution

Surely what ever type of differentiation you did (normal, partial etc.) all the parts would just end up being 0 so the differential is zero.

Can someone please set me straight.

Thanks,

Your example:
C = mV^-1
dC = ∂C/∂m dm + ∂C/∂V dV
so dC/dt = ∂C/∂m dm/dt + ∂C/∂V dV/dt.
But ∂C/∂m = 1/V and ∂C/∂V = -m/V²
So if you know how m and V vary with time you can compute dC/dt.

 

[Chestermiller]

You differentiate it using the quotient rule:

$$\frac{dC}{dt}=\frac{V\frac{dm}{dt}-m\frac{dV}{dt}}{V^2}=\frac{\frac{dm}{dt}-C\frac{dV}{dt}}{V}$$

Chet

 

[rezeew]

I can provide a response to your question about differentiating equations in physics. Differentiating an equation is a mathematical process that involves finding the rate of change of a variable with respect to another variable. In the case of your example, differentiating the equation C = m/V with respect to time would involve finding the rate of change of concentration with respect to time, which is also known as the concentration gradient.

To differentiate an equation, you can use the rules of differentiation, such as the power rule or the quotient rule. In the case of C = m/V, you would use the quotient rule because it involves dividing two variables. The result would be the rate of change of concentration with respect to time, which is also known as the concentration gradient.

Differentiating an equation in physics is important because it allows us to understand how one variable affects another variable in a given system. In your example, finding the concentration gradient would tell us how the concentration of a substance changes over time as the mass and volume of the system change.

I hope this helps to clarify the process of differentiating equations in physics. If you have any further questions, please let me know.