Question

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!

Answer 1

i guess you know how to find the derivate of x ... so just find for sqrt(x)

Answer 2

f(x) = \[\sqrt{x} -x \]

Answer 3

oh...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.

Answer 4

where you take the limit as h-->0

Answer 5

lim 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

Answer 6

seems he wants the increment thingy...the limits

Answer 7

@Ravus , are you asking to take the derivative using the definition? (limit definition of derivative)

Answer 8

@experimentX how do you get this sqrt(x+dx) = sqrt(x)*sqrt(1+dx/x)

Answer 9

@perl, nice avatar!

Answer 10

hehe

Answer 11

yes I want the "increment thingy"<<<thats exactally it! and yes dpalnc, I think it is the limit definition I mean.

Answer 12

@perl .. take x common!

Answer 13

huh?

Answer 14

plug it in to that...