How did $(x+y)^-2$ suddenly turn into that?
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[From Calculus Made Easy]
beginalign*
y+dy&=(x+dx)^-2\
&=x^-2left(1+fracdxxright)^-2
endalign*
Is there some formula I'm not aware of?
calculus
edited Aug 24 at 2:10
orion2112
404210
asked Aug 24 at 1:35
privilegedMale
132
add a comment |Â
up vote
0
down vote
favorite
[From Calculus Made Easy]
beginalign*
y+dy&=(x+dx)^-2\
&=x^-2left(1+fracdxxright)^-2
endalign*
Is there some formula I'm not aware of?
calculus
edited Aug 24 at 2:10
orion2112
404210
asked Aug 24 at 1:35
privilegedMale
132
Your picture does not match your title and is cut off. In the picture they just distribute $x^2$ out.
– Ross Millikan
Aug 24 at 1:55
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
[From Calculus Made Easy]
beginalign*
y+dy&=(x+dx)^-2\
&=x^-2left(1+fracdxxright)^-2
endalign*
Is there some formula I'm not aware of?
calculus
edited Aug 24 at 2:10
orion2112
404210
asked Aug 24 at 1:35
privilegedMale
132
[From Calculus Made Easy]
beginalign*
y+dy&=(x+dx)^-2\
&=x^-2left(1+fracdxxright)^-2
endalign*
Is there some formula I'm not aware of?
calculus
edited Aug 24 at 2:10
orion2112
404210
asked Aug 24 at 1:35
privilegedMale
132
edited Aug 24 at 2:10
orion2112
404210
edited Aug 24 at 2:10
orion2112
404210
edited Aug 24 at 2:10
orion2112
404210
404210
asked Aug 24 at 1:35
privilegedMale
132
asked Aug 24 at 1:35
privilegedMale
132
asked Aug 24 at 1:35
privilegedMale
132
132
Your picture does not match your title and is cut off. In the picture they just distribute $x^2$ out.
– Ross Millikan
Aug 24 at 1:55
add a comment |Â
Your picture does not match your title and is cut off. In the picture they just distribute $x^2$ out.
– Ross Millikan
Aug 24 at 1:55
Your picture does not match your title and is cut off. In the picture they just distribute $x^2$ out.
– Ross Millikan
Aug 24 at 1:55
Your picture does not match your title and is cut off. In the picture they just distribute $x^2$ out.
– Ross Millikan
Aug 24 at 1:55
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
It's a slight variation of the following trick:
$$ (a + b)^2 = left( a left(1 + frac ba right) right)^2 = a^2 left( 1 + frac ba right)^2$$
answered Aug 24 at 1:57
mweiss
17.3k23268
Is there a proof for this trick?
– privilegedMale
Aug 24 at 2:06
1
It's just the distributive property (you factor out an $a$ from both terms of the binomial) followed by the exponent rule $(ab)^n = a^n b^n$.
– mweiss
Aug 24 at 2:08
@privilegedMale A proof is just to evaluate both sides and show, that they are indeed even.
– Cornman
Aug 24 at 2:08
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
It's a slight variation of the following trick:
$$ (a + b)^2 = left( a left(1 + frac ba right) right)^2 = a^2 left( 1 + frac ba right)^2$$
answered Aug 24 at 1:57
mweiss
17.3k23268
Is there a proof for this trick?
– privilegedMale
Aug 24 at 2:06
1
It's just the distributive property (you factor out an $a$ from both terms of the binomial) followed by the exponent rule $(ab)^n = a^n b^n$.
– mweiss
Aug 24 at 2:08
@privilegedMale A proof is just to evaluate both sides and show, that they are indeed even.
– Cornman
Aug 24 at 2:08
add a comment |Â
up vote
3
down vote
accepted
It's a slight variation of the following trick:
$$ (a + b)^2 = left( a left(1 + frac ba right) right)^2 = a^2 left( 1 + frac ba right)^2$$
answered Aug 24 at 1:57
mweiss
17.3k23268
Is there a proof for this trick?
– privilegedMale
Aug 24 at 2:06
1
It's just the distributive property (you factor out an $a$ from both terms of the binomial) followed by the exponent rule $(ab)^n = a^n b^n$.
– mweiss
Aug 24 at 2:08
@privilegedMale A proof is just to evaluate both sides and show, that they are indeed even.
– Cornman
Aug 24 at 2:08
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
It's a slight variation of the following trick:
$$ (a + b)^2 = left( a left(1 + frac ba right) right)^2 = a^2 left( 1 + frac ba right)^2$$
answered Aug 24 at 1:57
mweiss
17.3k23268
It's a slight variation of the following trick:
$$ (a + b)^2 = left( a left(1 + frac ba right) right)^2 = a^2 left( 1 + frac ba right)^2$$
answered Aug 24 at 1:57
mweiss
17.3k23268
answered Aug 24 at 1:57
mweiss
17.3k23268
answered Aug 24 at 1:57
mweiss
17.3k23268
answered Aug 24 at 1:57
mweiss
17.3k23268
17.3k23268
Is there a proof for this trick?
– privilegedMale
Aug 24 at 2:06
1
It's just the distributive property (you factor out an $a$ from both terms of the binomial) followed by the exponent rule $(ab)^n = a^n b^n$.
– mweiss
Aug 24 at 2:08
@privilegedMale A proof is just to evaluate both sides and show, that they are indeed even.
– Cornman
Aug 24 at 2:08
add a comment |Â
Is there a proof for this trick?
– privilegedMale
Aug 24 at 2:06
1
It's just the distributive property (you factor out an $a$ from both terms of the binomial) followed by the exponent rule $(ab)^n = a^n b^n$.
– mweiss
Aug 24 at 2:08
@privilegedMale A proof is just to evaluate both sides and show, that they are indeed even.
– Cornman
Aug 24 at 2:08
Is there a proof for this trick?
– privilegedMale
Aug 24 at 2:06
Is there a proof for this trick?
– privilegedMale
Aug 24 at 2:06
1
1
It's just the distributive property (you factor out an $a$ from both terms of the binomial) followed by the exponent rule $(ab)^n = a^n b^n$.
– mweiss
Aug 24 at 2:08
It's just the distributive property (you factor out an $a$ from both terms of the binomial) followed by the exponent rule $(ab)^n = a^n b^n$.
– mweiss
Aug 24 at 2:08
@privilegedMale A proof is just to evaluate both sides and show, that they are indeed even.
– Cornman
Aug 24 at 2:08
@privilegedMale A proof is just to evaluate both sides and show, that they are indeed even.
– Cornman
Aug 24 at 2:08
add a comment |Â
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Your picture does not match your title and is cut off. In the picture they just distribute $x^2$ out.
– Ross Millikan
Aug 24 at 1:55