Author Topic: maths thread i guess (calculus is way cool(kek)) (Read 4323 times)

Nonnel · November 28, 2016, 07:02:40 PM

That which is derived

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Drydess · November 28, 2016, 07:23:17 PM

nevermind i can't read

ultimamax · November 28, 2016, 07:34:58 PM

A derivative represents the rate of change of some value.

For example, if I threw a ball at 5m/s in a vacuum without gravity then it would just fly in the direction I threw it at 5m/s forever. The derivative of its position (since speed is the rate of change of position) would be 5 at any given time.

Aide33 · November 28, 2016, 07:36:27 PM

Geometrically it is the slope of the line intersecting a certain point of a curve or a function

Like this:

Meaningfully, it is the rate at which the output variable (y) of a function changes in an instant. For example:

if y = x^2
from x = 0 to x2 = 2
the value of y changed by ((2^2) - (0^2))/2 = 2

so the rate of change between 0 and 2 is 4

the derivative is a way of getting a rate of change at an exact instant(or a single point) with no time interval

so let's say: x = 2 and now the second x is getting closer and closer to 2
so
x=2 x2=2.1000
x=2 x2=2.0100
x=2 x2=2.0001

if you do this forever the value between x and x2 get infinitely small so we can ignore it completely.

then if you calculate the rate of change between the two points x=2 and x2=2.0001 you get
(2.0001^2 - 2^2)/0.0001
which is approximately equal to 4, which is the slope of the line tangent to the point (2,4) on the graph y=x^2

if you have any questions, leave me a response, I typed this in like 5 minutes lol

auzman466 · November 28, 2016, 07:43:48 PM

A derivative expresses the slope of the tangent line of a point on a curve. A tangent line is simply a line that touches the curve.
Finding derivatives is a fundamental concept in calculus. It's used for graphing curves without a calculator, solving optimization (max/min) problems, finding rate of change at certain points on a curves, and much more that I haven't had the pleasure of doing yet/can't remember.

Quote from: Aide33 on November 28, 2016, 07:36:27 PM

Geometrically it is the slope of the line intersecting a certain point of a curve or a function

Like this:

Meaningfully, it is the rate at which the output variable (y) of a function changes in an instant. For example:

if y = x²
from x = 0 to 2x = 2
the value of y changed by ((2²) - (0²))/2 = 2

so the rate of change between 0 and 2 is 4

the derivative is a way of getting a rate of change at an exact instant(or a single point) with no time interval

so let's say: x = 2 and now the second x is getting closer and closer to 2
so
x=2 x2=2.1000
x=2 x2=2.0100
x=2 x2=2.0001

if you do this forever the value between x and x2 get infinitely small so we can ignore it completely.

then if you calculate the rate of change between the two points x=2 and x2=2.0001 you get
(2.0001² - 2²)/0.0001
which is approximately equal to 4, which is the slope of the line tangent to the point (2,4) on the graph y=x²

if you have any questions, leave me a response, I typed this in like 5 minutes lol

yep this nails it on the head

DrMobius · November 28, 2016, 10:36:03 PM

You you have some function f(x), the derivative of f(x) is f'(x) where f'(x) is the slope of f(x) at all points. Basically, the derivative measures the rate of change of a function

Tactical Nuke · November 29, 2016, 08:15:06 AM

rate of which slope is changing

take the derivative of y=2x and you get y'=2

which is the slope

Texan101 · November 29, 2016, 10:17:53 AM

Quote from: Tactical Nuke on November 29, 2016, 08:15:06 AM

rate of which slope is changing

take the derivative of y=2x and you get y'=2

which is the slope

The way to reach this is finding the limit of (f(x+h)-f(x))/h as h approaches 0. For xⁿ, it becomes nx^n-1

TristanLuigi · November 29, 2016, 10:33:24 AM

you guys nailed this pretty much but calculus is loving cool
it's the point where math becomes really interesting rather than just a death march

Nickelob Ultra · November 29, 2016, 12:06:54 PM

Quote from: TristanLuigi on November 29, 2016, 10:33:24 AM

you guys nailed this pretty much but calculus is loving cool
it's the point where math becomes really interesting rather than just a death march

Math would be so much more fun and so many more people would love it and pursue it if our education system didn't teach it like it is.

Lots of people find that they actually like math and the cool stuff you can figure out with it when you get away from the hammer and nail, plug and chug, and memorize everything type of stuff.

Ravencroft� · November 29, 2016, 12:11:17 PM

Quote from: TristanLuigi on November 29, 2016, 10:33:24 AM

you guys nailed this pretty much but calculus is loving cool
it's the point where math becomes really interesting rather than just a death march

To me it became the point of intolerance and mindlessly doing problems in a notebook for hours on end. Calculus is hell and I still can't believe I made it all the way through diff equations. Physics was a lot more fun because it actually made use of the concepts we learned in calc and applied them to laws, theories, cross-product derivations, etc.

Element · November 29, 2016, 04:37:25 PM

calculus is way cool and super useful, especially when applying it to a physics scenario

e-maxx · November 29, 2016, 04:39:00 PM

i never went past algebra 2

SubDaWoofer · November 29, 2016, 04:50:17 PM

Quote from: e-maxx on November 29, 2016, 04:39:00 PM

i never went past algebra 2

triggered

cooldawson3 · November 29, 2016, 06:04:55 PM

Quote from: e-maxx on November 29, 2016, 04:39:00 PM

i never went past algebra 2

Calculus is.... intense.