Derivatives?

Question

How do you process derivatives in mathematics? My sister is in Calculus, and requires to know Derivatives to pass the course, but due to the professor going under some illness or some sort, he wasnt able to teach the class/her, derivatives. Her exam is coming up, and doesnt have a grasp on it at all?

So to sum it up:

How would you explain derivatives in the simplest form?

I'm trying to help her with it, but only having Adv. 11 Mathematics, doesnt help much.

Can anybody help here?

Note: Her professor said quote: "The exam will not have limits, so you won't have to learn that."

Answer 1

I don't know why an exam would include derivatives but not limits, since derivatives are a type of limit.

There really isn't enough space here to sum up how to do a derivative. That's a subject for a good part of an entire pre-calc or calculus course. I'm sure somebody will post a few of the rules for taking derivatives of simple functions, like f(x) = x^3, but that doesn't explain how to do more complicated things like f(x) = sin^2 (4x + 5).

Here are a few pages though that sum up the concept:
http://mathforum.org/library/drmath/view/53398.html
http://mathforum.org/library/drmath/view/53407.html

Answer 2

For the derivative of a polynomial: ax^4+bx^3....
the derivative is just 4ax^3+3bx^2....you just multiply the coefficient by the power of the x and then reduce the power by 1.
Another example, if y=x^3+2x^2-x+2 then the derivative of y=3x^2+4x-1 note: for 2, pretend it is 2x^0 so the derivative is 0*2*x^(0-1)=0. Anyway, hope this helps.

Answer 3

Like Geezah, I'm nearly dumbfounded by your quote, since a derivative cannot be defined without limits. I've found Wolfram Mathworld to be an excellent resource for review and learning "new" concepts. You might try helping your sister memorize these derivatives and rules, which is what the professor seems to be requiring:

http://mathworld.wolfram.com/Derivative.html

Answer 4

For some special functions
there are derivative rules
Try to learn and use them

Example

y=ln u

y'=u'/u

Hint: Find a list for the derivative rules.
search google.
And you may ask me your questions
[e-mail]

Answer 5

These Formulas can help.

Derivative Formulas
1. If f(x)=C (where C is a constant) then f(x)=0
2. If f(x) = x^n then f ’(x)= n (x^ n-1)
3. If h(x) = k (x^n) then f ’(x)= nk (x^ n-1)
4. If h(x) = f(x) ± g(x) then h’(x)= f ’(x) ± g’(x)
Product Rule
5. If h(x) = f(x) g(x) then h’(x)= f (x) g’(x)+g(x)f ’(x)
Quotient Rule
6. If h(x) = f(x) /g(x) then h’(x)= g(x)f ’(x)-f (x) g’(x)/ (g(x)^2)

Answer 6

In the simplest form, if y is a function of x (ie if y changes as x changes), then the derivitive of y with respect to x

dy/dx = change in y / small change in x
Let's say x changes from a to b and y changes from ya to yb
then dy/dx = (yb - ya) / (b-a)

eg if y = x^2
Let's say x changes from x to x+dx
Then y changes from y to y+dy
y = x^2
y+dy = (x+dx)^2
= x^2 + 2x*dx + dx^2
Since dx is small, dx^2 can be neglected
So y+dy = x^2 + 2x*dx
dy = 2x*dx
because y = x^2
dy/dx = 2x

Answer 7

go away 6 out first. pondering x^4/a million-x write x^4= x^3*x, so as that we are in a position to write the expression as x^3(x+a million-a million)/a million-x. separate it out like x^3(x-a million)/a million-x+x^3/a million-x, this leads to (-x^3)+(x^3/a million-x) because of fact the utmost ability of this expression is 3 and you should locate the fourth by-product so all would be 0.

Answer 8

Search the web for : "defintion of mathematical derivatives." You will find defintions, explanations and examples.