Math Help - Beginner Implicit Differentiation Question

1. Beginner Implicit Differentiation Question

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?

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

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

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

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

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

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

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

However, according to the answer sheet I have, the correct answer is...
$(-6x / 5y)$

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...)

2. Re: Beginner Implicit Differentiation Question

You simply did not simplify by dividing the numerator and denominator by their common factor of 2.

Your working was correct, you just need to reduce the fraction to its lowest terms.

3. Re: Beginner Implicit Differentiation Question

Originally Posted by MarkFL2
You simply did not simplify by dividing the numerator and denominator by their common factor of 2.

Your working was correct, you just need to reduce the fraction to its lowest terms.
That's embarrassing...Thank you!!