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anonymous
 4 years ago
derivative of:
sqrt(x)  x
using the first principal. Please show work. The answer should be 1/[2*sqrt(x)]1
I cant get the minus 1!
anonymous
 4 years ago
derivative of: sqrt(x)  x using the first principal. Please show work. The answer should be 1/[2*sqrt(x)]1 I cant get the minus 1!

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experimentX
 4 years ago
Best ResponseYou've already chosen the best response.0i guess you know how to find the derivate of x ... so just find for sqrt(x)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0f(x) = \[\sqrt{x} x \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh...so just do them one at a time?: That actually makes a lot of sense. the problem is I have the equation in the "definition of the derivative formula" and its not simplifying down right.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0where you take the limit as h>0

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.0lim dx>0 (sqrt(x+dx)  sqrt(x))/dx now sqrt(x+dx) = sqrt(x)*sqrt(1+dx/x) using binomial expansion, and removing higher terms  close to linear expression we have: sqrt(x)(1+1/2*dx/x) or, lim dx>0 (sqrt(x)(1+1/2*dx/x)  sqrt(x))/dx or, lim dx>0 (1/2*dx/sqrt(x))/dx = 1/(2sqrt(x)) hence proved

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0seems he wants the increment thingy...the limits

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@Ravus , are you asking to take the derivative using the definition? (limit definition of derivative)

perl
 4 years ago
Best ResponseYou've already chosen the best response.0@experimentX how do you get this sqrt(x+dx) = sqrt(x)*sqrt(1+dx/x)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes I want the "increment thingy"<<<thats exactally it! and yes dpalnc, I think it is the limit definition I mean.

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.0@perl .. take x common!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1333351654824:dw plug it in to that...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yeah I did plug it in, and I get the right answer almost. I get 1/2*sqrt(x) but that whole thing should have a "1"! i dont get that bit

perl
 4 years ago
Best ResponseYou've already chosen the best response.0@experimentX (x+dx)^1/2 = x^1/2 ( 1 + dx/x ) ^1/2

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.0dx is supposed to be del x ... or better h

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1333351804706:dw do some algebra here....

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok... too many cooks... i'll quit.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yeah I know what the formula is, but the algebra is giving me trouble

perl
 4 years ago
Best ResponseYou've already chosen the best response.0@experimentX Very clever argument, so you looked at the binomial series and took the first two terms (linear )

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.0yes .. since dx^higer would be very less ... it would seem better to take linear term.

perl
 4 years ago
Best ResponseYou've already chosen the best response.0then you factored out sqrt x

experimentX
 4 years ago
Best ResponseYou've already chosen the best response.0yes .. and that would cancel out .. sqrt(x) leaving dx/(2sqrt(x)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0omg wow finally got it. simple algebra really. lmfao............

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1333354174909:dw
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