Question

I have doubt..., I'm totally sure that Partial Derivate respect x (and with the other variables but don't change the result, obviously just the variable in the numerator)
f(x, y, z) = Log(Sqrt(4 - x² - y² - z²)) is
x / Sqrt(4 - x² - y² - z²)
I calculated in Wolfram Mathematica program and the result was: -x / (4 - x² - y² - z²)
Am I wrong?...

Answer 1

i think you are off by a minus sign

Answer 2

the derivative of \(-x^2\) is \(-2x\)

Answer 3

and of course
\[\log(\sqrt{\xi})=\frac{1}{2}\log(\xi)\]

Answer 4

I've calculated it of this way:
∂f/∂x = \[1/ \sqrt{4 - x² - y² - z²} * (-2x) * (-1/2)(4 - x² - y² -z²)^{-3/2}) = (-2x) * -1/2(4 - x² - y² -z²)^{3/2} * 1/ \sqrt{4 - x² - y² - z²}\]

Answer 5

you lost me,
pull the one half out front, it will certainly be easier

Answer 6

It shows an incomplete eq ... -.-
We have the minus of internal derivative of -x² " - 2x "
and the minus sign of 1/2 (by deriving the root in the denominator) right?

Answer 7

There's no way for that result, and multiplying the root of the Log derivative with the term ^ 3/2 that's equals to \[\sqrt{4 - x² - y² z²}\]

Answer 8

(same base, plus exponents 1/2 + 3/2 = 2)
... Really I will have
x / (4 - x² - y² - z²) ² right?
Sorry, the first result was incorrect, there's not a root (1/2 in the exponent of denominator, just 2...)
Have I something wrong? ... :(