Hello,

My online unit is up to implicit differentiation, and I thought I had a good grasp on it, but the first question has already thrown me off. Could somebody explain exactly where my misunderstanding comes from?

The question asks

Find dy/dx by implicit differentiation for the following...

$\displaystyle 6x^2 + 5y^2 = 36$

This is my working for this problem, as I understood based off the material I have...

$\displaystyle d/dx (6x^2) - d/dx(5y^2) = d/dx(36) $

$\displaystyle 12x + 10y (dy/dx) = 0$

$\displaystyle = 10y (dy/dx) = - 12x$

$\displaystyle = dy/dx = (-12x / 10y)$

However, according to the answer sheet I have, the correct answer is...

$\displaystyle (-6x / 5y)$

Now, I don't know if I'm misunderstanding what the question is asking, because I'm essentially learning without the help of a teacher/tutor (except for this website), so I've quite often misunderstood certain aspects of this calculus course, but I was under the impression that solving this equation was via the steps I had above - that is, differentiate in respect to x, assuming that y is a function of x.

The answer that I can see almost seems like there's been no differentiation used (ie: no power rule used that I can see...)

Help please.