[OT] WAY OFF TOPIC...math guys...how abuot some help please

[Zakath]

Ok...its alittle embarassing that im in Calculus and i forgot how to handle fraction exponents...lol
anyways im having trouble trying to remember how factor (actually extract) them out of an equation...here is it...

those of you who have a graphing calculator or know how to work one will understand this equation better...cause thats pretty much how im setting it up...


F'(x) = [(X^2 + 1)^-1/2] - [ (X^2)(X^2 + 1)^-3/2]


there is more to how i got to this step but anyways this is where i am.....i am finding the derivative...which is the equation above..but im trying to simplify it...and well i need to extract to something like

F'(x) = [ (X^2 + 1)^-3/2 ] [ (X^2 + 1)^? - (X^2) ]

ok...well thats about as much as i can really do..cause i dont remember the rest....*laughs* ofcourse you know i can find the critcal numbers and increasing and decreasing and inflection points...but uhh i need to get through this step...if for nothing else so i know how to do it when i come across it again...lol..thanks

 

[Claude Raines]

Ok...its alittle embarassing that im in Calculus and i forgot how to handle fraction exponents...lol
anyways im having trouble trying to remember how factor (actually extract) them out of an equation...here is it...

those of you who have a graphing calculator or know how to work one will understand this equation better...cause thats pretty much how im setting it up...


F'(x) = [(X^2 + 1)^-1/2] - [ (X^2)(X^2 + 1)^-3/2]


there is more to how i got to this step but anyways this is where i am.....i am finding the derivative...which is the equation above..but im trying to simplify it...and well i need to extract to something like

F'(x) = [ (X^2 + 1)^-3/2 ] [ (X^2 + 1)^? - (X^2) ]

ok...well thats about as much as i can really do..cause i dont remember the rest....*laughs* ofcourse you know i can find the critcal numbers and increasing and decreasing and inflection points...but uhh i need to get through this step...if for nothing else so i know how to do it when i come across it again...lol..thanks

F'(x) = [ (X^2 + 1)^-3/2 ] [ (X^2 + 1) - (X^2) ]

which is:

F'(x) = [ (X^2 + 1)^-3/2 ]

 

[oliverhenshaw]

I'm not sure if you've specified where you're going with this, but getting between the two steps you've shown is easy.

x^-n = 1 / x^n

is true where the exponent, n, is a fraction or not.
But I expect you know that.
To see what to do, it's simplest (and saves space for me) to define a convenient variable,

a = (x^2 + 1)^1/2

So your equation can be written

f'(x) = a^-1 - x^2 * a^-3
= a^-3 * (a^2 - x^2)

and you've got no fractions inside the bracket and can put a back in and find things cancelling out like the first person to reply did.

Wish I'd noticed that.

 

[physics_ninja]

Whenever factoring subtract the exponent of the factor from the exponents of the other terms. Note that this will give you a zero exponent in the term that is being factored out. Also, beware of your negative signs, they can screw up even a simple problem.

So in this case we have:

-1/2 - (-3/2) = 2/2 and - 3/2 - (- 3/2) = 0.

Also, you can find a common denominator and subtract the fractions first.

 

[oliverhenshaw]

extra

and from how the first line you've got looks, you might have been better off using the chain rule. Might.

d(uv)/dx = vdu/dx + udv/dx

or, more relevantly,

d(u/v)/dx = 1/v^2 * (vdu/dx - udv/dx)

Or it might help with similar problems.

 

[Zakath]

Basic what i was saying is that where i have that ? mark at....is what i need to know to put there...what exponent would it be and why...because i forgot what it would be.....the original problem i got this derivitive from was

F(x) = (X)/ ( X^2 +1)^1/2
the key board doesnt have a square root sign....so i moved it to a fraction....then before i broke down the problem into a derivative i move the bottom part up by making the exponent negitive...so it came out as
F(x) = (X) ( X^2 + 1) ^-1/2
then i found the derivative.....which is qouted below....

F'(x) = [(X^2 + 1)^-1/2] - [ (X^2)(X^2 + 1)^-3/2]


there is more to how i got to this step but anyways this is where i am.....i am finding the derivative...which is the equation above..but im trying to simplify it...and well i need to extract to something like

F'(x) = [ (X^2 + 1)^-3/2 ] [ (X^2 + 1)^? - (X^2) ]

 

[Claude Raines]

Basic what i was saying is that where i have that ? mark at....is what i need to know to put there...what exponent would it be and why...because i forgot what it would be.....the original problem i got this derivitive from was

At the question mark the exponent is one (1). When multiplying a^n * a^m = a^(n+m). Thus -3/2 + 1 = -1/2.

 

[SableWyvern]

Good thread, Zakath. I was just wondering the same thing myself the other day....

 

[Zakath]

Thanks guys..thanks everyone! i knew you guys cuold help me pull through..