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need some math help

P

platinumike

Platinum Member
Its actually for calculus and were doing derivatives. The original problem:

y=x^2 (squareroot)1-x^2

which is read as: y equals x squared times the square root of 1- x squared

I rewrite it, do the product rule for derivatives and end up with this:

-x^3(1-x^2)^-1/2 + 2x(1-x^2)^-1/2

Iam stuck at this point. Apparently the book is factoring out one of thoose quantities raised to the -1/2 and getting this answer:

x(1-x^2)^-1/2 ( (-x^2(1)+2(1-x^2) )

I feel like im gonna get no replies the way i typed this out, worth a try though! apprarently its factoring that i didnt learn in algebra.
 
Originally posted by: platinumike
is it a crime to ask for help?
Click to expand...

To people who don't know they answer it is.

To me, I don't mind helping someone if they've shown they put the effort into it.
 
My bro would probably p!ss all over that...but alas I don't have ihs Maths skills so I can't help you out 🙁

Other guys, give the guy some help if you can. No point in telling him to do his own homework...

Koing
 
I've put the effort into this. I've been working on this for the past 30 minutes. You honestly think I would put no effort into this problem and type it out here on atot and waitfor a response? that actually seems easier? I type it here because I have no clue and you guys are great at math.
 
Just factor it out yourself. You'll get the book's answer.

Edit: Wait, you have a minus sign error.
 
I can do this, I know I can, but what is square root? Is it the same as root? Like:

Square root of 16 = 4, because 4^2 = 16?

If so, I'll do this 😛.
 
Ok... you need to first you the product rule, and then the chain rule...

hold on... I'll elaborate...
 
thank you. Yes I used the product rule and the chain rule, do a little bit of simplifying and I get stuck at that point.

EDIT: had to edit what i said here before, i was wrong.
 
If the math looks awful, and you think you can't do it, then simplify. Let z = (1-x^2)^0.5. Then the problem becomes this:

y = x^2 * z

Take the derivative: y' = 2x*z + x^2*z' = 2x*z - x^3/z. Note your minus sign error here in the exponent.

Simplify: y' = x*(2z-x^2/z) = x/z*(2z^2-x^2) = matches the book.
 

Let f(x) = x^2, g(x) = (1-x^2)^.5. Then y = f(x) * g(x)

By the product rule:

y' = f'(x) * g(x) + g'(x) * f(x).

Now f'(x) = 2x.

To calculate g'(x), we now use the chain rule:

Let m(x) = 1 - x^2, n(x) = x^.5 . Thus, g(x) = m( n(x) ). By the chain rule,
g'(x) = m'( n(x) ) * n'(x). The deriviate of m and n are
m'(x) = -2x and n'(x) = .5 * x^(-.5). Hence

g'(x) = -2( .5 * x^(-.5)) = - x^(-.5).

So,

y' = 2x * (1 - x^2)^.5 + x^2 * (- x^(-.5))
= 2x * (1 - x^2)^.5 - x^(1.5)


You can simplify from there...

 
You guys are weird. I think my solution is much better, although unfinished. (I'm only 15, though, and this should exceed any knowledge I have 😉.)

y = (x^2)(sqrt(1-(x^2)))
y^2 = (x^4)(1-(x^2))
y^2 = x^4 - x^6
y = sqrt(x^4 - x^6)

My TI-83 thinks it's correct, but I can't simplify it any further 🙁.
Can you take it from here?
 
Originally posted by: Vegitto
You guys are weird. I think my solution is much better, although unfinished. (I'm only 15, though, and this should exceed any knowledge I have 😉.)

y = (x^2)(sqrt(1-(x^2)))
y^2 = (x^4)(1-(x^2))
y^2 = x^4 - x^6
y = sqrt(x^4 - x^6)

My TI-83 thinks it's correct, but I can't simplify it any further 🙁.
Can you take it from here?
Click to expand...

Great, so you didn't take a single derivative and we are, like Maxine Nightingale says, right back where we started from.
 
Originally posted by: chuckywang
Originally posted by: Vegitto
You guys are weird. I think my solution is much better, although unfinished. (I'm only 15, though, and this should exceed any knowledge I have 😉.)

y = (x^2)(sqrt(1-(x^2)))
y^2 = (x^4)(1-(x^2))
y^2 = x^4 - x^6
y = sqrt(x^4 - x^6)

My TI-83 thinks it's correct, but I can't simplify it any further 🙁.
Can you take it from here?
Click to expand...

Great, so you didn't take a single derivative and we are, like Maxine Nightingale says, right back where we started from.
Click to expand...

So x^4 - x^6 can't be simplified? My math world is collapsing!
 
Originally posted by: Vegitto
You guys are weird. I think my solution is much better, although unfinished. (I'm only 15, though, and this should exceed any knowledge I have 😉.)
Click to expand...
It does exceed the knowledge you have. He is NOT solving for y. He is solving for the slope of the y vs x graph for ALL positions of x.
 
Originally posted by: Vegitto
Originally posted by: chuckywang
Originally posted by: Vegitto
You guys are weird. I think my solution is much better, although unfinished. (I'm only 15, though, and this should exceed any knowledge I have 😉.)

y = (x^2)(sqrt(1-(x^2)))
y^2 = (x^4)(1-(x^2))
y^2 = x^4 - x^6
y = sqrt(x^4 - x^6)

My TI-83 thinks it's correct, but I can't simplify it any further 🙁.
Can you take it from here?
Click to expand...

Great, so you didn't take a single derivative and we are, like Maxine Nightingale says, right back where we started from.
Click to expand...

So x^4 - x^6 can't be simplified? My math world is collapsing!
Click to expand...

*repeatedly pounds head into keyboard*
 
Originally posted by: dullard
Originally posted by: Vegitto
You guys are weird. I think my solution is much better, although unfinished. (I'm only 15, though, and this should exceed any knowledge I have 😉.)
Click to expand...
It does exceed the knowledge you have. He is NOT solving for y. He is solving for the slope of the y vs x graph for ALL positions of x.
Click to expand...

Oh, he wants x?
Easy.

x^4 - x^6 = 0
x^4 = x^6
x = 0
 
Originally posted by: chuckywang
Originally posted by: Vegitto
Originally posted by: chuckywang
Originally posted by: Vegitto
You guys are weird. I think my solution is much better, although unfinished. (I'm only 15, though, and this should exceed any knowledge I have 😉.)

y = (x^2)(sqrt(1-(x^2)))
y^2 = (x^4)(1-(x^2))
y^2 = x^4 - x^6
y = sqrt(x^4 - x^6)

My TI-83 thinks it's correct, but I can't simplify it any further 🙁.
Can you take it from here?
Click to expand...

Great, so you didn't take a single derivative and we are, like Maxine Nightingale says, right back where we started from.
Click to expand...

So x^4 - x^6 can't be simplified? My math world is collapsing!
Click to expand...

*repeatedly pounds head into keyboard*
Click to expand...

Sorry dude, I just tried to help..
 
Originally posted by: Vegitto
Originally posted by: chuckywang
Originally posted by: Vegitto
Originally posted by: chuckywang
Originally posted by: Vegitto
You guys are weird. I think my solution is much better, although unfinished. (I'm only 15, though, and this should exceed any knowledge I have 😉.)

y = (x^2)(sqrt(1-(x^2)))
y^2 = (x^4)(1-(x^2))
y^2 = x^4 - x^6
y = sqrt(x^4 - x^6)

My TI-83 thinks it's correct, but I can't simplify it any further 🙁.
Can you take it from here?
Click to expand...

Great, so you didn't take a single derivative and we are, like Maxine Nightingale says, right back where we started from.
Click to expand...

So x^4 - x^6 can't be simplified? My math world is collapsing!
Click to expand...

*repeatedly pounds head into keyboard*
Click to expand...

Sorry dude, I just tried to help..
Click to expand...

He wants dy/dx, ie the derivative of y with respect to x, ie y'. He does not want to solve for y or whatever you were trying to do.
 
Originally posted by: Vegitto
Then what does he want?
Click to expand...
From the original post: "and were doing derivatives".

From my first response to you: "slope of the y vs x graph".

Take your pick. They mean the same thing.

 
Originally posted by: dullard
Originally posted by: Vegitto
Then what does he want?
Click to expand...
From the original post: "and were doing derivatives".

From my first response to you: "slope of the y vs x graph".

Take your pick. They mean the same thing.
Click to expand...

Oh, wait! I know. I don't know what it's called in English, though 🙁.. And I don't think I can give the answer if the only possible outcomes are x=-1 through x=1 and y=0 consistently..
 
Originally posted by: Vegitto
Originally posted by: chuckywang
Originally posted by: Vegitto
Originally posted by: chuckywang
Originally posted by: Vegitto
You guys are weird. I think my solution is much better, although unfinished. (I'm only 15, though, and this should exceed any knowledge I have 😉.)

y = (x^2)(sqrt(1-(x^2)))
y^2 = (x^4)(1-(x^2))
y^2 = x^4 - x^6
y = sqrt(x^4 - x^6)

My TI-83 thinks it's correct, but I can't simplify it any further 🙁.
Can you take it from here?
Click to expand...

That's nice to try to help, but you shouldn't help if you have no idea what you're talking about.

Great, so you didn't take a single derivative and we are, like Maxine Nightingale says, right back where we started from.
Click to expand...

So x^4 - x^6 can't be simplified? My math world is collapsing!
Click to expand...

*repeatedly pounds head into keyboard*
Click to expand...

Sorry dude, I just tried to help..
Click to expand...

 
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