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

In summary: This post is directed at the original poster, lLovePhysics]Wow, I guess I messed up on the "with respect to" part too. =[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...This post is directed at the original poster, lLovePhysics]
  • #1
lLovePhysics
169
0
I need to find the derivative of: [tex] f(t)=-2t^{2}+3t-6[/tex]

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

My Solution:

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

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?
 
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  • #2
This is the way to do it:

[tex]\frac{d}{dt} [-2t^{2}] {+\frac{d}{dt}[3t]-\frac{d}{dt}6[/tex]
 
  • #3
oomg I messed up on all of the problems =/
 
  • #4
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
bob1182006 said:
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..
 
  • #6
well no but I mean if you write [tex]\frac{d(f(x))}{dx}[/tex]it's the same as writing [tex]\frac{d}{dx}f(x)[/tex] 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 >.<
 
  • #7
Good you know TeX, just didn't want to confuse lLovePhysics by doing things unproper =)
 
  • #8
This post is directed at the original poster, lLovePhysics

malawi_glenn said:
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.

[tex]f'(t) = \frac{df(t)}{dt}[/tex]

and

[tex]f'(x) = \frac{df(x)}{dx}[/tex]

are both correct. But

[tex]f'(t) = \frac{df(t)}{dx}[/tex]

is wrong.


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

[tex]\frac{df(t)}{dx}[/tex]
 
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  • #9
This post is directed at the original poster, lLovePhysics

malawi_glenn said:
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

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

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 [itex]d/dt[/itex] 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.
 
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  • #10
Hurkyl said:
Well, yes and no. At your level of sophistication, it's best to think of

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

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 [itex]d/dt[/itex] 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..
 
  • #11
malawi_glenn said:
You must have confused me with the original poster..
Yes, I did.
 
  • #12
Hurkyl said:
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.

[tex]f'(t) = \frac{df(t)}{dt}[/tex]

and

[tex]f'(x) = \frac{df(x)}{dx}[/tex]

are both correct. But

[tex]f'(t) = \frac{df(t)}{dx}[/tex]

is wrong.


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

[tex]\frac{df(t)}{dx}[/tex]

Wow, I guess I messed up on the "with respect to" part too. =[
 
  • #13
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 :)
 

1. How do I find the derivative of a function?

To find the derivative of a function, you need to first identify the function's independent variable and then use the rules of differentiation to find the derivative. These rules include the power rule, product rule, quotient rule, and chain rule.

2. What is the purpose of finding the derivative of a function?

The derivative of a function represents the rate of change of the function at a specific point. It can also help us find the slope of a tangent line to the function's graph and determine the function's concavity and critical points.

3. How do I know if I have found the correct derivative?

You can check if you have found the correct derivative by taking the derivative of the original function and comparing it to the derivative you have calculated. They should be equal if you have found the correct derivative.

4. What are some common mistakes when finding the derivative of a function?

Some common mistakes when finding the derivative of a function include forgetting to apply the chain rule, using the power rule incorrectly, and not simplifying the final answer. It is also important to pay attention to the signs and use parentheses when necessary.

5. How do I practice and improve my skills in finding derivatives?

The best way to practice and improve your skills in finding derivatives is to work on a variety of problems, starting from simpler functions and gradually moving on to more complex ones. You can also use online resources or textbooks to find practice problems and check your solutions.

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