How do I correctly use differentiation operators in equations?

[caljuice]

Hey. I am pretty confused on how to use differentation operators (dy/dx,d/dx), what does it mean in equations and how do I know when it means i should find the derivative of something. Word problems are confusing me on how to use these and when to find derivatives. I always thought differentation operators mean find the derivative.

Like to find velocity, i get it by v=dx/dt of the position a function. And finding the derivative of the position function gives me the velocity function.
s(position)=(t^3)-(6t^2)+9t

so to find V, I:
v=(ds/dt)=3t^2-12t+9

But in another example, even though i have differentation operators, i don't seem to need to find the derivative...

V=5.3/P, where v is volume and p is pressure. Find the rate of change of V with respect to P when P is 50 kpa.

(dv/dp)=-5.3/(p^2)
=-5.3/25000=-0.00212

Sorry if I'm unclear. Basically I guess, I'm asking how to use differentation operators and when i should find the derivative when they are present in an equation.

 

[HallsofIvy]

Hey. I am pretty confused on how to use differentation operators (dy/dx,d/dx), what does it mean in equations and how do I know when it means i should find the derivative of something. Word problems are confusing me on how to use these and when to find derivatives. I always thought differentation operators mean find the derivative.

Like to find velocity, i get it by v=dx/dt of the position a function. And finding the derivative of the position function gives me the velocity function.
s(position)=(t^3)-(6t^2)+9t

so to find V, I:
v=(ds/dt)=3t^2-12t+9

But in another example, even though i have differentation operators, i don't seem to need to find the derivative...

V=5.3/P, where v is volume and p is pressure. Find the rate of change of V with respect to P when P is 50 kpa.

(dv/dp)=-5.3/(p^2)
=-5.3/25000=-0.00212

Sorry if I'm unclear. Basically I guess, I'm asking how to use differentation operators and when i should find the derivative when they are present in an equation.

I don't understand your second example. You say "But in another example, even though i have differentation operators, i don't seem to need to find the derivative...", but you certainly did find the derivative! You seem to know perfectly well how to use the differentiation operators (your spelling of "differentiation" could use some work!) and I can only say "find the derivative when you are asked to find it!", as you are in both of these examples.

Can you give an actual example in which there is a differentiation operator but you don't have to differentiate? Perhaps you are thinking of a situation where you are given the derivative of a function and asked to find the derivative (i.e. anti-derivative)?

 

[caljuice]

oops my bad. I'm embarassed. I see the second example is actually the quotient rule now. Got confused over nothing.
I kept thinking dv/dp meant v divide by P.
Which also gave (5.3/p)/p = 5.3/P^2?
So differentiation operators do mean find the derivative. I keep thinking differentiation operators as regular fractions.Thanks, and I can spell differentiation now.

 

[HallsofIvy]

oops my bad. I'm embarassed. I see the second example is actually the quotient rule now. Got confused over nothing.
I kept thinking dv/dp meant v divide by P.
Which also gave (5.3/p)/p = 5.3/P^2?
So differentiation operators do mean find the derivative. I keep thinking differentiation operators as regular fractions.Thanks, and I can spell differentiation now.

You see, this the problem with the internet. If you were sitting in front of me, I could whack you over the head with a two-by-four!