Anonymous at Fri, 28 Jun 2024 20:14:42 UTC No. 16258659

Another way to describe a derivative function is the difference between Y divided by the difference between X. Don't they teach that in the second year of middle school any more?

Anonymous at Fri, 28 Jun 2024 20:16:02 UTC No. 16258661

>>16258659
You didn't answer my question.

Anonymous at Fri, 28 Jun 2024 20:29:11 UTC No. 16258682

>>16258639
The power rule applies to polynomials and expressions with rational and irrational exponents. Image related

Anonymous at Fri, 28 Jun 2024 20:30:58 UTC No. 16258685

>>16258682
My bad. Let me commit sudoku

Anonymous at Fri, 28 Jun 2024 20:34:56 UTC No. 16258688

>>16258685
I give up, I guess I'm the mathlet now.

Anonymous at Fri, 28 Jun 2024 20:36:01 UTC No. 16258690

>>16258682
I don't really understand all of that. I am new to math. What other ways are there to get a derivative besides the power rule?

Anonymous at Fri, 28 Jun 2024 20:39:23 UTC No. 16258693

>>16258639
do you remember how the power rule is deduced?
the same applies to >>16258685, trigonometric functions, and the logarithm but with more tricks. and you'll learn them sooner or later.

Anonymous at Fri, 28 Jun 2024 20:45:02 UTC No. 16258704

>>16258693
Can you answer this>>16258690

Also I don't quite understand trigonometry yet. I understand there is a Unite Circle divided into 4 quadrants and it is measured in radians not degrees. And I learned from Algebra that an identity is an equation with more than one answer, but I don't fully understand it yet. I am still learning.

Anonymous at Fri, 28 Jun 2024 21:04:08 UTC No. 16258720

>>16258704
I think the article you quoted lists all that's required.
e.g. (e^x)' = e^x, (sinx)' = cosx, ...

not so many rules are really required to solve questions involving derivative, because all functions are known to be essentially written as "ax^n + bx^(n-1) + cx^(n-2)+...."

Anonymous at Fri, 28 Jun 2024 21:33:58 UTC No. 16258752

>>16258639
Look up the definition of the derivative. The power rule is just a special case of that.

Do you know how limits work?

Anonymous at Fri, 28 Jun 2024 21:43:50 UTC No. 16258758

>>16258639
[eqn]f'(x)=\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/eqn]This is the derivative of the function f at the point x assuming that the limit exists. You can derive
>product rule
>chain rule
>derivative of inverse function
using this limit.

Anonymous at Fri, 28 Jun 2024 22:47:53 UTC No. 16258850

>>16258720
So there's only like
>Power Rule.
>Sum and Difference Rule. ...
>Constant Multiple Rule. ...
>Product Rule. ...
>Quotient Rule. ...
>Chain Rule.
Those are all the rules or ways to get a derivative? Are there any more?

Anonymous at Fri, 28 Jun 2024 22:49:05 UTC No. 16258853

>>16258752
>Do you know how limits work?
Hardly. Not really lol. I know of them though. I just don't really understand them. I think I'm making progress though.

Anonymous at Fri, 28 Jun 2024 23:27:25 UTC No. 16258916

>>16258850
There are more rules to derivatives, like the derivative of other trigonometric functions, like tan:

[eqn](\tan{x})' = \frac{1}{\cos^2{x}} = \sec^2{x}[/eqn]

The aforementioned rules are the most useful rules to find a derivative to begin with. There are a lot of other rules, but as for an introduction to derivatives, these rules are sufficient. As you learn more, you find more rules. I suggest finding resources to learn more about this. Buy an introductory book to calculus, or find a series on youtube, so on.

>>16258853
If you don't have much knowledge about limits, this is pretty much required to understand what the derivative is. I also suggest you learn about trigonometry, exponential functions, linear functions, finding the rate of change in linear functions, Euler's number, logarithms, and the natural logarithm if you haven't already. This isn't necessary for understanding what the derivative is, but it is necessary to understand the derivative of functions that include these things.

A word of caution though: Limits can be difficult to understand, this is because the actual definition of limits have to be well-defined. If you find yourself ending up in something called "epsilon-delta proofs", then you're probably too deep in the rabbit hole for the time being. You don't really have to go this deep to understand limits.

Anonymous at Fri, 28 Jun 2024 23:30:39 UTC No. 16258922

>>16258850
Those are the ones that make sense with the algebra taught in school. Any algebraic expression can have it's derivative taken using those rules. When you add a new function, it comes with a new rule, unless it can be described by existing rules. It all comes back to the limit definition.

Anonymous at Fri, 28 Jun 2024 23:33:02 UTC No. 16258926

>>16258916
We'll, technically I think you can show that any operator which is linear and obeys leibniz is identical to the derivative, so you may be able to derive all of the rules without limit definition.

Anonymous at Fri, 28 Jun 2024 23:43:12 UTC No. 16258942

>>16258926
There are genuine algebraic approaches to the derivative without using limits, like using the set of hyperreal numbers.
However, they still get the same result, and as far as I can tell, still rely on infinitesimal values in some way or another to arrive at the same conclusion. The rules of derivation stay the same, no matter which of these notations or approaches you use.
Limits are just the traditional and standard way of teaching derivatives, because they lead well into epsilon-delta proofs at a higher level of math education, as well as other types of proofs.