Finding the derivative of a function. Am I doing this right?

[lLovePhysics]

I need to find the derivative of: f(t)=-2t^{2}+3t-6

However, I do not know if I'm writing it out correctly. Please tell me if I'm doing anything wrong, thanks!

My Solution:

\frac{d[-2t^{2}]}{dx}+\frac{[3t]}{dx}-\frac{d[6]}{dx}

Is that the correct way to write it out? Do you just "factor" out the terms and make them individual derivative functions?

Basically, differentiation rules are the same as limit rules except for the mutliplication and division right?

 

[malawi_glenn]

This is the way to do it:

\frac{d}{dt} [-2t^{2}] {+\frac{d}{dt}[3t]-\frac{d}{dt}6

 

[lLovePhysics]

oomg I messed up on all of the problems =/

 

[bob1182006]

not really what you have is right it's just when you get into longer equations you don't want to be writing out d(.....)/dt since it's easier to write d/dt *(...).

the's the same as 3/2=3*1/2

 

[malawi_glenn]

not really what you have is right it's just when you get into longer equations you don't want to be writing out d(.....)/dt since it's easier to write d/dt *(...).

the's the same as 3/2=3*1/2

hmm so you are saying that the differential operator is MULTIPLIED with a function?

"d/dt *(...) "

The thing I was concerned most of in lLovePhysics post was that he took the derivative of a function of variable t with respect to x..

 

[bob1182006]

well no but I mean if you write \frac{d(f(x))}{dx}it's the same as writing \frac{d}{dx}f(x) but usually you don't want f(x) up there since you can have like a square root, fraction, etc...which can get pretty weird if you have to draw that line and then dx >.<

 

[malawi_glenn]

Good you know TeX, just didn't want to confuse lLovePhysics by doing things unproper =)

 

[Hurkyl]

This post is directed at the original poster, lLovePhysics[/color]

The thing I was concerned most of in lLovePhysics post was that he took the derivative of a function of variable t with respect to x..

Well, the problem asks for the derivative of f, right?

So, if I use a dummy variable to represent the argument to f, then I should be differentiating with respect to that same dummy variable. i.e.

f&#039;(t) = \frac{df(t)}{dt}

and

f&#039;(x) = \frac{df(x)}{dx}

are both correct. But

f&#039;(t) = \frac{df(t)}{dx}

is wrong.


Of course, if you were asked to differentiate f(t) with respect to x, then the correct expression is

\frac{df(t)}{dx}

 

[Hurkyl]

This post is directed at the original poster, lLovePhysics[/color]

hmm so you are saying that the differential operator is MULTIPLIED with a function?

"d/dt *(...) "

Well, yes and no. At your level of sophistication, it's best to think of

\frac{d}{dt}[ f(t) ]

as one gigantic symbol with two arguments: the dummy variable at the bottom (t, in this example), and the expression to differentiate (f(t), in this example).

When you become more mathematically sophisticated, you might have reason to treat d/dt as an entity all by itself. At that time, you will learn a new kind of product operation that makes sense here. But it has nothing to do with the multiplication operation you are familiar with.

 

[malawi_glenn]

Well, yes and no. At your level of sophistication, it's best to think of

\frac{d}{dt}[ f(t) ]

as one gigantic symbol with two arguments: the dummy variable at the bottom (t, in this example), and the expression to differentiate (f(t), in this example).

When you become more mathematically sophisticated, you might have reason to treat d/dt as an entity all by itself. At that time, you will learn a new kind of product operation that makes sense here. But it has nothing to do with the multiplication operation you are familiar with.

How do you know my level of sophistication? You must have confused me with the original poster..

 

[Hurkyl]

You must have confused me with the original poster..

Yes, I did.

 

[lLovePhysics]

This post is directed at the original poster, lLovePhysics[/color]


Well, the problem asks for the derivative of f, right?

So, if I use a dummy variable to represent the argument to f, then I should be differentiating with respect to that same dummy variable. i.e.

f&#039;(t) = \frac{df(t)}{dt}

and

f&#039;(x) = \frac{df(x)}{dx}

are both correct. But

f&#039;(t) = \frac{df(t)}{dx}

is wrong.


Of course, if you were asked to differentiate f(t) with respect to x, then the correct expression is

\frac{df(t)}{dx}

Wow, I guess I messed up on the "with respect to" part too. =[

 

[malawi_glenn]

This will become essiential when you are entering multi varible calculus, i.e when your function might be f(x,y) = 2xy + x^2 ; then it matters a lot what variable you are interested in, so it's good to be careful from the very beginning :)