Math

[Chronicle 164]

What is integration?

If you know what differentiation is, then integration is pretty much the inverse method to differentiation. Do quote this message if you want me to explain integration using a problem. 

[thethiefofvictory 339]

If you know what differentiation is, then integration is pretty much the inverse method to differentiation. Do quote this message if you want me to explain integration using a problem. 

Quoted.

[Chronicle 164]

Quoted.

Sneaky  <_<. Meh, ok give me a question. I cannot seem to find my workbook.  

[thethiefofvictory 339]

Sneaky  <_<. Meh, ok give me a question. I cannot seem to find my workbook.  

 

Do quote this message if you want me to explain integration using a problem. 

^that. 

 

Although, how about calculus?

[Chronicle 164]

^that. 

 

Although, how about calculus?

Calculus? from that branch all I took was differentiation and integration. Do you mean the rules of integration calculus? 

[LOLKILLERTOTHEDEATH 1,921]

If you know what differentiation is, then integration is pretty much the inverse method to differentiation. Do quote this message if you want me to explain integration using a problem. 

I don't know if I know what differentiation is. Perhaps you can help me assess how much I do. I know about the product, chain, power and quotient rules. I also know that a few functions (such as e^x and sin(x)) have unique derivatives. 

 

So with integration, does that mean you get the slope of a function and you anti-derrive it?

[Chronicle 164]

So with integration, does that mean you get the slope of a function and you anti-derrive it?

Sorry for the late reply, Let's begin with differentiation then. 

 

I personally find differentiating a term in the form ax^n straightforward. Assuming n is a positive integer, differentiate y = 5x^4 + 7x^3 - 6x^2 + 3x -2.

Rather than explaining everything in one sitting, I'd rather you do some of the work yourself and I'll guide you through the question. Although there are different methods to differentiate, so tracking which one you are using should be tough, I'm up for the challenge though. 

 

 Differentiate y = 5x^4 + 7x^3 - 6x^2 + 3x -2

[LOLKILLERTOTHEDEATH 1,921]

Sorry for the late reply, Let's begin with differentiation then. 

 

I personally find differentiating a term in the form ax^n straightforward. Assuming n is a positive integer, differentiate y = 5x^4 + 7x^3 - 6x^2 + 3x -2.

Rather than explaining everything in one sitting, I'd rather you do some of the work yourself and I'll guide you through the question. Although there are different methods to differentiate, so tracking which one you are using should be tough, I'm up for the challenge though. 

 

 Differentiate y = 5x^4 + 7x^3 - 6x^2 + 3x -2

Would that be:

 

20x^3 + 21x^2 -12x+3

 

?

[Chronicle 164]

Would that be:

 

20x^3 + 21x^2 -12x+3

 

?

Correct, Now differentiate with fraction types:

 

   y = (5x^3 -7x -1) / x^2

[LOLKILLERTOTHEDEATH 1,921]

Correct, Now differentiate with fraction types:

 

   y = (5x^3 -7x -1) / x^2

\frac{\left(5x^4+7x^2-2x\right)}{x^4}

[Guest]

 

 Differentiate y = 5x^4 + 7x^3 - 6x^2 + 3x -2

Dy/DX = 5 (4x^3) + 7(3x^2)- 6 (2x) + 3 + 0

= 20x³ + 21x² - 12x + 3

[Guest]

Correct, Now differentiate with fraction types:

 

   y = (5x^3 -7x -1) / x^2

Does this have a diff method? Or like the normal routine. Idk I studied this one month ago, and I forgot the rules/ formulae.

[Chronicle 164]

\frac{\left(5x^4+7x^2-2x\right)}{x^4}

Simplified? I don't know how you got that

Does this have a diff method? Or like the normal routine. Idk I studied this one month ago, and I forgot the rules/ formulae.

There are multiple methods, they all give you the same answer 

 

Edit: For fraction types, I only know of two methods. 

Edited July 24, 2018 by Chronicle

[Guest]

Simplified? I don't know how you got that

There are multiple methods, they all give you the same answer 

 

Edit: For fraction types, I only know of two methods. 

I guess the first one is that one formula from which we derive other formulae? I guess the second one. For multiplication i guess the UV rule is correct r8? u.f(v) + v.f(u)?

[Chronicle 164]

I guess the first one is that one formula from which we derive other formulae? I guess the second one. For multiplication i guess the UV rule is correct r8? u.f(v) + v.f(u)?

There are formula's which you have to remember yes, the product and quotient rules have that "UV" so I guess so.

[LOLKILLERTOTHEDEATH 1,921]

Simplified? I don't know how you got that

 

There are multiple methods, they all give you the same answer 

 

Edit: For fraction types, I only know of two methods.

 

I meant (5x^4 + 7x^2 - 2x)/ x^4

 

I tried to use the quotient rule, so I may or may not have done so properly.

[Chronicle 164]

I meant (5x^4 + 7x^2 - 2x)/ x^4

 

I tried to use the quotient rule, so I may or may not have done so properly.

I've never tried the quotient rule on fraction type questions, can't tell you myself. The answer for the fraction type question was 5 + (7/x^2) + (2/x^3)

Do you know how I got there? or shall I go through it? I only know two methods that can be used, would you like to see both of them side by side or would just one of them do the job? 

[LOLKILLERTOTHEDEATH 1,921]

I've never tried the quotient rule on fraction type questions, can't tell you myself. The answer for the fraction type question was 5 + (7/x^2) + (2/x^3)

Do you know how I got there? or shall I go through it? I only know two methods that can be used, would you like to see both of them side by side or would just one of them do the job?

 

Please do show me!

Please do show me!

I think our answers are almost the same. Mine appears to just not be fully simplified.

[Guest]

Please do show me!

 

I think our answers are almostthe same. Mine Ppears to just not be fully simplified.

Well, I would have helped but hey, I have to revise everything then.

[Chronicle 164]

Please do show me!

Ok, here goes: 

 

y = (5x^3 -7x -1) / x^2 

 

I'm not sure if you've learnt this but, when we have y = ax^n, ∴ dx/dy = anx^n -1. You'll need it later on.

 

We can "break" the denominator from the equation and simply multiply it instead. Like so:

 

 1/x^2 (5x^3 -7x -1) / x^2.

 

Assuming you know the laws of indices, the 1/x^2 can be written as x^-2. We use that instead of the unpleasant fraction.

 

x^-2 (5x^3 -7x -1), Now we simply expand by multiplying the outside by the inside. This gives us: 

 

5x -7x^-1 -x^ -2. 

 

Here's where most people get confused, see that equation I said we'll need later? Notice how we have matching forms to y = ax^n.

 

Well, ∴ dx/dy = 5 + 7x^-2 + 2x^3. Here we use the laws of indices again, this leaves us with the following: 

 

5 + 7(1/x^2) + 2(1/x^3), sometimes they ask you to leave it in this form, but lets go the extra mile. 

 

We expand the brackets that need expanding, the final answer 5 + 7/x^2 + 2/x^3. 

 

So, where did I lose you? 

[LOLKILLERTOTHEDEATH 1,921]

Ok, here goes: 

 

y = (5x^3 -7x -1) / x^2 

 

I'm not sure if you've learnt this but, when we have y = ax^n, ∴ dx/dy = anx^n -1. You'll need it later on.

 

We can "break" the denominator from the equation and simply multiply it instead. Like so:

 

 1/x^2 (5x^3 -7x -1) / x^2.

 

Assuming you know the laws of indices, the 1/x^2 can be written as x^-2. We use that instead of the unpleasant fraction.

 

x^-2 (5x^3 -7x -1), Now we simply expand by multiplying the outside by the inside. This gives us: 

 

5x -7x^-1 -x^ -2. 

 

Here's where most people get confused, see that equation I said we'll need later? Notice how we have matching forms to y = ax^n.

 

Well, ∴ dx/dy = 5 + 7x^-2 + 2x^3. Here we use the laws of indices again, this leaves us with the following: 

 

5 + 7(1/x^2) + 2(1/x^3), sometimes they ask you to leave it in this form, but lets go the extra mile. 

 

We expand the brackets that need expanding, the final answer 5 + 7/x^2 + 2/x^3. 

 

So, where did I lose you?

 

I don't belive you did. I somehow got the right answer. Thanks for helping me!

[Chronicle 164]

I don't belive you did. I somehow got the right answer. Thanks for helping me!

Guess it was unfinished, well done! Hands over cookie

 

Are you familiar with the reverse chain rule? it's pretty much integration (by substitution) also known as U-substitution. I'll help you with integration first though, wanted to know if you are familiar with these methods so I know what to write. 

[Hancho 3,902]

 

 

[ThirdOnion 4,898]

I also know that a few functions (such as e^x and sin(x)) have unique derivatives. 

Out of curiosity, what do you mean by "unique derivatives?" If you mean that they are can't be obtained using chain/quotient/product/ rules etc, it should be noted that those rules are "shortcuts" - generalizations of the steps in which you determine the instantaneous rate of change and technically not the steps themselves.

Edited July 25, 2018 by ThirdOnion

[LOLKILLERTOTHEDEATH 1,921]

Out of curiosity, what do you mean by "unique derivatives?" If you mean that they are can't be obtained using chain/quotient/product/ rules etc, it should be noted that those rules are "shortcuts" - generalizations of the steps in which you determine the instantaneous rate of change and technically not the steps themselves.

I just mean to say exactly that. I mean that the power, quotient and other rules end up not being of very much use in taking their derrivatives.