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Bryanluxor
 one year ago
why does: y+dy=(x+dx)^2 equal:
=x^2(1+dx/x)^2
Bryanluxor
 one year ago
why does: y+dy=(x+dx)^2 equal: =x^2(1+dx/x)^2

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RaphaelFilgueiras
 one year ago
Best ResponseYou've already chosen the best response.0put x in evidence

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

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

atlas
 one year ago
Best ResponseYou've already chosen the best response.2simplify it to x^2 (1+dx/x)^2 I hope it makes sense now

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0I stiil dont get it Could someone please explain it step by step?

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[x+dx=x+\frac{x}{x} dx=x+x \cdot \frac{dx}{x}=x(1+\frac{dx}{x})\]

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0how can x+dx be written as x(1+dx/x)?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[(x+dx)^{2}=[(x)(1+\frac{dx}{x})]^{2}=x^{2}(1+\frac{dx}{x})^{2} \]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Did you see what I said above what you said?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1dw:1387637203504:dw

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1dw:1387637215111:dw

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1you can factor out that x

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1You wanted step by step I'm looking at the inside, x+dx, right now.

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1which i already did above

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0i dont understand why x+dx=x(1+dx/x)

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0where did you get the 1?

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

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0and how did you get dx/x?

myininaya
 one year ago
Best 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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1you should see an x in both terms now

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1you can factor an x out

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0how did you get x/x?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[x(1+\frac{1}{x}dx)\] \[x(1+\frac{dx}{x}) \]

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1If you factor something out you are dividing the terms you factor from

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0im sorry but i dont understnad

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

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0Can you please write down every step you do and how you get every variable?

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0in one answer please

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1If you don't understand it separately how do you expect to understand it together?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Do you understand the example I just put?

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Do you know the distributive property?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Like a(b+c) means ab+ac

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1That is the distributive property

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1You 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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1What 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: \[ac(\frac{ab}{ac}+\frac{ac}{ac})=ac(\frac{b}{c}+1)\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1What do you get when you multiply out the ac(b/c+1) expression?

OOOPS
 one year ago
Best ResponseYou've already chosen the best response.0I 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 ?

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

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0the aim is to differentiate y=x^2

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0the second equal sign is the result

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0once we have powered the left hand side of the equation to 2

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0what do you mean by "ODE?"

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

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

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0ill post the page in a sec

Bryanluxor
 one year ago
Best ResponseYou've already chosen the best response.0he adds dy or dx to expand it a bit

OOOPS
 one year ago
Best ResponseYou've already chosen the best response.0I 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 :((

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