# Homework Help: Finding the derivative of a function. Am I doing this right?

1. Sep 29, 2007

### 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?

2. Sep 29, 2007

### malawi_glenn

This is the way to do it:

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

3. Sep 29, 2007

### lLovePhysics

oomg I messed up on all of the problems =/

4. Sep 29, 2007

### 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

5. Sep 29, 2007

### malawi_glenn

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..

6. Sep 29, 2007

### 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 wierd if you have to draw that line and then dx >.<

7. Sep 29, 2007

### malawi_glenn

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

8. Sep 29, 2007

### Hurkyl

Staff Emeritus
This post is directed at the original poster, lLovePhysics

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.

$$f'(t) = \frac{df(t)}{dt}$$

and

$$f'(x) = \frac{df(x)}{dx}$$

are both correct. But

$$f'(t) = \frac{df(t)}{dx}$$

is wrong.

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

$$\frac{df(t)}{dx}$$

Last edited: Sep 29, 2007
9. Sep 29, 2007

### Hurkyl

Staff Emeritus
This post is directed at the original poster, lLovePhysics

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.

Last edited: Sep 29, 2007
10. Sep 29, 2007

### malawi_glenn

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

11. Sep 29, 2007

### Hurkyl

Staff Emeritus
Yes, I did.

12. Sep 29, 2007

### lLovePhysics

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

13. Sep 29, 2007

### 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 begining :)

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