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

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

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

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

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

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

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

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

Bryanluxor
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1which i already did above

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

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

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

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

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

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

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

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

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

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

myininaya
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0in one answer please

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

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

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

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

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

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

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

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

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

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

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

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

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

OOOPS
 2 years 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
 2 years 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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