What's a derivative, exactly? t. not knower

Google it

Wander back to /b/

>>8262497
Your mother
You're mother
Your mother
Yes.

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>>8262502
>>8262500
Stop bullying pls

OP are you serious or trolling?

I don't want to waste my time explaining if you don't really need it.

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>>8262507
I'm serious.

>>8262497
A derivative is a word that represents a mathematical concept, which is an approximation of a property of nature

>>8262509
Do you know something about limits?

>>8262513
A bit.

>>8262518
It's the slope of the tangent line to a curve at a particular point on the curve

Formally, you can define it with limits

But knowing the definition and the table of derivatives is enough

You know what a slope is right? It's basically how "steep" a curve is, roughly. The derivative of a function if basically a function itself that gives you the slope at each point (plug in the x,and you get the slope at that corresponding point).

>>8262529
>>8262523
I think I understand, thanks.

>>8262544

YouTube has some good videos on it, check it out. There's a lot you can do with just knowing how derivatives work.

>>8262544
You claim to understand limits so here's a little limit defintion of the derivative.
[eqn]\lim_{h\to 0} \frac{f(x+h) - f(x)}{h}[/eqn]
Obviously, for computing derivatives, you won't be writing out this defintion and perform every tiny step. We have nice little shortcuts such as the power rule, quotient rule, and the most important: chain rule.

>>8262558

>newfriend here

How do you type math notation like that?

>>8262561
This website uses a little neat markup called [math]\LaTeX[/math]. There's quite a bit about latex though, so much that anyone can write up an entire book about it.

Returning to your question, to input latex (that fancy math notation you just saw), you just sandwich any latex syntax into the tags [math] or [eqn]. You use [math] for having it inlike [math]\text{like this}[/math] and you use [eqn] for the bigger stuff: [eqn]\huge{\text{like this}}[/eqn].

To get the limit defintion of what I rendered, you simple sandwich something like the following into either [math] or [eqn]:

\lim_{h\to 0} \frac{f(x+h) - f(x)}{h}

>>8262573

[math]\lim_{h\to 0} \frac{f(x+h) - f(x)}{h}[math]

>>8262592

w8 I failed [math] \lim_{h\to 0} \frac{f(x+h) - f(x)}{h} [math]

>>8262593
You're supposed to treat these like XML tags in that you close your tag with </foo>

For instance:
<math>. . .</math>

Where < and > is [ and ].

>>8262601

[math] \lim_{h\to 0} \frac{f(x+h) - f(x)}{h} [/math]

>>8262497
a derivative is the rate at which something changes.

For example, the derivative of a position function is the rate at which the position changes, AKA the velocity

>>8262601

Thanks senpai

>>8262605
i should clarify, it is the INSTANTANEOUS rate at which something changes. The rate at that specific instant

IGNORE THIS POST:

[math] (x^2) + (y^2) = 50 [/math]

>>8262611
now solve for x and y

>>8262618

[math] x = sqrt(50 - (y^2)) [/math]

>>8262620

I gotta get used to the syntax
Try 2:

[math] x = (50 - (y^2))^(1/2) [/math]

>>8262620
try "\sqrt" instead of "sqrt"

>>8262623
Use http://mathb.in/ as your sandbox (or the TeX button in the reply windows here).

Reference of LaTeX commands: http://www.artofproblemsolving.com/wiki/index.php/LaTeX:Commands

>>8262630
>>8262623
[math]\sqrt{like+this+my+nigga}[/math]

>>8262633
[eqn]\sqrt{\text{like this my nigga}}[/eqn]

>>8262632
[latex][math]\sqrt{test}[/math][/latex]

>>8262558
And to provide a specific example of how the definition of a derivative can be applied:
Given [math]f(x)=x^3[/math], we have
[eqn]f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}=\lim_{h\to 0}\frac{(x+h)^3-x^3}{h}=\lim_{h\to 0}\frac{x^3+3x^2h+3xh^2+h^3-x^3}{h}
=\lim_{h\to 0}(3x^2+3xh+h^2)=3x^2[/eqn]
In practice, there are a lot of simple rules that can be derived this way, such as [math]\frac{d}{dx}x^n=nx^{n-1}[/math], so resorting to the definition is rarely necessary.

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>>8262497
A derivative is the idea that if you take a slope and keep zooming in that you will eventually see a straight line.