Question

Calculus 3

No 6

Answer 1

@IrishBoy123

Answer 2

Probably I could help, but not without some review.
I've seen this question posted before, with the recommendation from one user that the "Implicit Function Theorem" be used. Are you familiar with this Theorem, and if so, have you applied it before to problem solving?

Answer 3

Yes I have applied the implicit function theorem to simpler question.

Answer 4

What have you done s o far to attack the problem at hand?

Answer 5

let me post what I have.

Answer 6

I see the given relationship has three terms. The first involves y. Simply apply the power rule to obtain the partial derivative with respect to y of this first term.

Answer 7

one way to see it:

\(F(xyz) = \sqrt{3y} - y \cos (yx) - 2x + 3 z^2\)
so \(dF= 0= dx[ y^2 \sin (yx) - 2] + dy[ \frac{1}{2}\sqrt{3}\frac{1}{\sqrt{y}} - \cos (yx) + xy\sin (yx) ] + dz[ 6z ] \)

dx = 0

and we already have dF = 0

Answer 8

but if you know differentials, you can just throw it out, ....., i think !!!!

depends really on what you know.

Answer 9

@IrishBoy123 its cos(xz) not cos(yx)

Answer 10

implicit function theorem @mathmale