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RaphaelFilgueirasBest ResponseYou've already chosen the best response.0
put x in evidence
 3 months ago

atlasBest ResponseYou've already chosen the best response.2
Another way of thinking is divide the expression on R.H.S with x^2 and then multiply it with x^2 on the outside
 3 months ago

atlasBest ResponseYou've already chosen the best response.2
multiplying and dividing Right hand side with x^2 \[\frac{ x ^{2}(x+dx)^{2} }{ x^{2} }\] \[x^{2} (\frac{ x+dx }{ x })^{2}\]
 3 months ago

atlasBest ResponseYou've already chosen the best response.2
simplify it to x^2 (1+dx/x)^2 I hope it makes sense now
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
I stiil dont get it Could someone please explain it step by step?
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
Ok, do you agree that x+dx could be written as x(1+dx/x)?
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
\[x+dx=x+\frac{x}{x} dx=x+x \cdot \frac{dx}{x}=x(1+\frac{dx}{x})\]
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
how can x+dx be written as x(1+dx/x)?
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
\[(x+dx)^{2}=[(x)(1+\frac{dx}{x})]^{2}=x^{2}(1+\frac{dx}{x})^{2} \]
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
Did you see what I said above what you said?
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
dw:1387637203504:dw
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
dw:1387637215111:dw
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
you can factor out that x
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
but how did you get to x+x d/x? the equation is (x+dx)^2
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
You wanted step by step I'm looking at the inside, x+dx, right now.
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
If you can understand why x+dx=x(1+dx/x) we can move on to the exponent part
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
which i already did above
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
i dont understand why x+dx=x(1+dx/x)
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
where did you get the 1?
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
Like do you the distributive property. It says: a(b+c)=ab+ac
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
and how did you get dx/x?
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
\[x+dx=x+\frac{x}{x} dx \] look I multiply dx by x/x which is just one
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
you should see an x in both terms now
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
you can factor an x out
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
how did you get x/x?
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
\[x(1+\frac{1}{x}dx)\] \[x(1+\frac{dx}{x}) \]
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
I just put it there so you would see better x/x is there if you write it because it is just one
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
If you factor something out you are dividing the terms you factor from
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
im sorry but i dont understnad
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
For example \[3x+9=3(\frac{3x}{3}+\frac{9}{3})=3(x+3)\] Do you understand this example?
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
Can you please write down every step you do and how you get every variable?
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
in one answer please
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
If you don't understand it separately how do you expect to understand it together?
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
Do you understand the example I just put?
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
You might want to review factoring then. Because all I did was factor 3x+9 in that example
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
Do you know the distributive property?
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
Like a(b+c) means ab+ac
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
That is the distributive property
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
You can look at it either way. a(b+c)=ab+ac ab+ac=a(b+c) Do you see on this side they say hey both of these terms have an a in common so let's factor it out
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
What they are doing when they factor is pulling something out (multiplying) and then also dividing by what they pulled out. Like for example , ab+ac we could factor factor out ac but that means we also need to divide each term by ac like this: \[ac(\frac{ab}{ac}+\frac{ac}{ac})=ac(\frac{b}{c}+1)\]
 3 months ago

myininayaBest ResponseYou've already chosen the best response.1
What do you get when you multiply out the ac(b/c+1) expression?
 3 months ago

OOOPSBest ResponseYou've already chosen the best response.0
I don't understand what we are supposed to do, re read your post, y +dy = (x+dx)^2 equal = x^2(1+dx/x)^2 can you use the draw box below to write it again ?
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
\[y+dy=(x+dx)^{2} =x ^{2}(1+\frac{ dx }{ x })^{2}\]
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
the aim is to differentiate y=x^2
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
the second equal sign is the result
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
once we have powered the left hand side of the equation to 2
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
what do you mean by "ODE?"
 3 months ago

OOOPSBest ResponseYou've already chosen the best response.0
one more question: from which course , you have this problem?
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
its from a book called calculus made easy, ill post the page i found it on right now
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
ill post the page in a sec
 3 months ago

BryanluxorBest ResponseYou've already chosen the best response.0
he adds dy or dx to expand it a bit
 3 months ago

OOOPSBest ResponseYou've already chosen the best response.0
I can understand (x +dx)^(2) = x^(2)(1+dx/x)^2 but from y +dy , I cannot see how they get the right hand side. since y = x^2 > dy = 2x^3 y + dy = x^2  2 x^3 = x^2(12dx/x) which is not their right hand side :((
 3 months ago

zpupsterBest ResponseYou've already chosen the best response.0
this might clear it up i like this book his proofs are easier to understand than the way was taught.
 3 months ago
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