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Halbrecht
1 year ago

1/ (2*root(x)) * (x-1) + root(x)

Use your knowledge

1/ (2*root(x)) * (x-1) with QR by making (x-1)^-1 / (2*root(x)) out of it

or QR and apply the PR for the denominator

w(x) you can already

IA3007
1 year ago

For the first summand: Use product rule.
For the second, can simply derive.

It is: f(x) = (x-1) * x ^ (-0.5) / 2 + x ^ (+0.5)

The following applies to the derivation: f’(x) = x ^ (-0.5) / 2 – (x-1) * x ^ (-1.5) / 4 + 0.5 * x ^ (-0.5) = 1/Wurzel(x) – (x-1) / (4*x*Wurzel(x)).

svwluke
1 year ago

If I have not made a mistake, it is:

1/Wurzel(x) – (x-1)/(4*x^(3/2)))

IA3007
1 year ago
Reply to  svwluke

Yeah, I got that too.