anyone help me with a basic calculus problem?

[Sage]

For some reason I cannot get this darned thing to work out right...

Differentiate:
Sq.Rt. (x + sq.rt. (x) )

It seems to me like it should be:

1 / [ 4 * sq.rt.(x + sq.rt. (x)) * sq.rt. (x) ]

BUT, calculator indicates:

[2 * sq.rt. (x) + 1] / [4 * sq.rt. (x) * sq.rt. {sq.rt. (x) + (sq.rt. (x) + 1) } ]

I cannot figure out what the heck i'm doing wrong. I'm using chain rule and differentiating whole function, to get 1 / [2 * sq.rt. {x + sq.rt. (x) } ] for the first function, then 1 / [2 * sq.rt. (x) ] for the second one, multiplying them to get the above result. I tried graphing them on the calculator and comparing the slope of the tangent line, as computed by my calculator, of the initial function at x=0.75 and it matches the value of what my calculator indicates if the correct derivative at x=0.75 but it does not match what my work indicates is correct.

Would greatly appreciate any help.

 

[K.I.L.E.R]

To calculate the 7th order PDE...

I got it:

g(x) = x + x^0.5
q(a) = a^0.5

g'(x) = 1 + 0.5*x^-0.5 = 1 + 1/(2*sqrt(x))
q'(a) = 0.5*a^-0.5 = 1/2*sqrt(a)

q'(a)*g'(x) = 1/2*sqrt(a) * 1 + 1/(2*sqrt(x))
= 1/2*sqrt(x + sqrt(x)) * (1 + 1/2*sqrt(x))

I love maths.
Want to play again?

 

[pcchen]

]then 1 / [2 * sq.rt. (x) ] for the second one

It should be 1 + 1/(2*sqrt(x)) for the second one.

 

[K.I.L.E.R]

I got it first.
I got it before you did.

It should be 1 + 1/(2*sqrt(x)) for the second one.

 

[Sage]

thanks guys, I already figured it out with the help of my mommie

 

[K.I.L.E.R]

Then why ask us if you're going to ask others first?
I wasted a page in my book for that.

 

[Sage]

Then why ask us if you're going to ask others first?
I wasted a page in my book for that.

Well, because I gave upon her helping me but then she called me back.