Question

what is the derivative of f(x)=
-2|x|^1/2

Answer 1

use the chain rule:
d/dx (-2 abs(x)^(1/2))
=-2 d/dx(abs(x)^(1/2))
=-2 * 1/2 * abs(x)^(-1/2) * d/dx (abs(x))
=-abs'(x)/sqrt(abs(x))
abs'(x)=x/abs(x);
=-x/(|x| sqrt(|x|))

Answer 2

this assumes the domain of f is the reals; f(x) is not a holomorphic function

Answer 3

so if we have 2|x|^1/2

would it look like:
=2 d/dx(abs(x)^(1/2))
=2 * 1/2 * abs(x)^(-1/2) * d/dx (abs(x))
=abs'(x)/sqrt(abs(x))
=abs'(x)=x/abs(x);
=x/(|x| sqrt(|x|))

or did i mess something up? @eashy

Answer 4

looks good :)

Answer 5

thanks