# Thread: What does a derivative do? Why use derivatives?

1. ## What does a derivative do? Why use derivatives?

Okay, Im 4th yr university, and i havent used calc in 4yrs

I can do derivates, but now im doing economics and somehow they are applying derivates to it.

I have a midterm on wednesday, so i am trying to understand how/why they are using derivates.

Can someone please explain what a derivate solves?

thanks.

Cellplanman

2. In calculus (a branch of mathematics) the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point; for example, the derivative of the position of a vehicle with respect to time is the instantaneous velocity at which the vehicle is traveling. Conversely, the integral of the velocity over time is the vehicle's position.

Derivative - Wikipedia, the free encyclopedia

3. Originally Posted by Cellplanman
Okay, Im 4th yr university, and i havent used calc in 4yrs

I can do derivates, but now im doing economics and somehow they are applying derivates to it.

I have a midterm on wednesday, so i am trying to understand how/why they are using derivates.

Can someone please explain what a derivate solves?

thanks.

Cellplanman
economics, huh?

here's something you should know ... define marginal cost.

4. Originally Posted by binomialbrother
In calculus (a branch of mathematics) the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point; for example, the derivative of the position of a vehicle with respect to time is the instantaneous velocity at which the vehicle is traveling. Conversely, the integral of the velocity over time is the vehicle's position.

Derivative - Wikipedia, the free encyclopedia
When I think how much quantity is changing at a given point i think:

(delta x - delta y) / delta y
Originally Posted by skeeter
economics, huh?

here's something you should know ... define marginal cost.
yea... see i've been barely scrapping by uni and HS without knowing very much...

heck in 1st yr I went into a calc exam without knowing what a quadratic was... i had to get a tutor to explain to me HS math since i never learned it. ( i didnt know what MX + B was)

Figured if this is my last year i need to get my marks up and actually learn something... therefore understanding the WHY or exactly what it does helps me learn the best, even if its the most basic thing ever

5. it is used to calculat the rate of change of a function. maybe puttng it in economics context will help. Say $y=$value of property and $x=$time. And say that the value of the property increases exponentially with time, simply, $y=x^2$ value in pounds, time in years.

$f(x)=x^2$
$f'(x)=2x$ the differentiated function ( $dy/dx$)
now, say you want to calculate how much the property is increasing at a given point, this can be done by putting in the value of $x$,, lets say, 20 years.

$f'(20)=2*20$
$f'(20)=40$
So at 20 years, the property value is increasing by 40 pounds.
obviously the figures are inaccurate with regards to our current economic climate, but, give or take!

6. see this is my issue.

I completly understand your steps in solving the derivative. but what i dont understand is why a derivative was used to solve the issue.

Like what made you set it up with

f ( x) = x^2?

oh yea, and the course i am doing is called:

EC310 - ECONOMICS AND GENDER

lol... if you want to see course website

http://www.tammyschirle.org/teaching...009/EC310.html

7. i just used $y=x^2$
because that was just a simple function to simulate the growth of a property price.

8. Like i've seen that equation many many many times. Solved in a zillion times (with variations in question)

but my main problem is i dont understand why. why does y = x^2 solve this question? what does a derivative do

also this might be easier on msn or gchat? lmk if u think so.. or we can just keep posting back and forth here

9. i can't, i'm on my ipod,
a derivative reduces the function whereby the gradient of the line at a point can be found, which makes it possible to discover the rate of change. if you're interested in the history of this then have a look over "differentiation from first principles", or "Liebniz Notation", and "liebniz" in particular.

10. Its not the history that i am looking for but rather why we use it. like in which situations would i want to use a 1st derivative vs a 2nd derivative vs a diff method?

11. well the first derivative offers the rate of change, and the second derivative is to find the acceleration of a function. for example, a racecar is travelling through a racetrack. the speed = time^2 - 1
when you differentiate that you see that the rate of change in speed = 2 * time (metres per second)
differentiate this again, and you'll see that the acceleration = 2 (metres per second per second)
sorry if i can't help

12. Originally Posted by binomialbrother
well the first derivative offers the rate of change, and the second derivative is to find the acceleration of a function. for example, a racecar is travelling through a racetrack. the speed = time^2 - 1
when you differentiate that you see that the rate of change in speed = 2 * time (metres per second)
differentiate this again, and you'll see that the acceleration = 2 (metres per second per second)
sorry if i can't help
hmm I vaguely remember something similar to this from back in my calc days.

I think what my problem is im not understanding what "rate of change" is.

13. the rate of change means, in the previous example, how many metres per second the speed changes, per second...? if you get me

14. Originally Posted by binomialbrother
the rate of change means, in the previous example, how many metres per second the speed changes, per second...? if you get me
lol... the more i respond to you, the dumber i feel.

how many meters per second the speed changes is acceleration no? which is 2nd derivative

15. i apologise that i'm having difficulty describing it.... the rate of change measures the gradient of the slope of the curve, and the acceleration is the speed at which the gradient changes...?

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