Differential Calculus: Find y' of y = ln( (6x^2) + (5y^2) )?

Question

I have these two problems i cant solve and I'd like some help with them, I already posted the other one. If you could post the steps you take to get the answer it would help me alot in understanding the concept of this. They provide me with these answers.

1. y' = 12y / 6x^2 + 5y^2 - 5y
2. y' = 12x / 6x^2 + 5y^2 - 10y
3. y' = 10x / 6x^2 + 5y^2 - 10y
4. y' = 10y / 6x^2 - 5y^2 + 5y
5. y' = 10x / 6x^2 - 5y^2 + 10y
6. y' = 12x / 6x^2 - 5y^2 + 5y

Answer 1

e^y = 6x^2+5y^2
y'e^y = 12x +10yy'
y'e^y -10yy' = 12x
y' = 12x/(e^y -10y)

Answer 2

Will supply 3 solutions : a million) using " man_mus_" thoughts the answer is [ a million - (a million / y)e^(x / y)] / [ 2y - (x / y^2) e^(x / y)]. note the version from his answer. 2) Take a by-product of your expression : y ' ln (x - y^2) + y (a million / {x - y^2} ) [a million - 2 y y '] = a million . remedy for y ' ; y ' = [ ( x - y^2) - y] / [( x - y^2) ln ( x - y^2) - 2 y^2] using that ln (x - y^2) = x / y the y ' might want to be written as [ x y - y^3-y^2] / [x^2 - x y- 2 y^3].....if those "solutions" are to comprise the answer then you extremely have copied the mission incorrectly

Answer 3

y' = 1/(6x^2+5y^2) * (12x+10y*y')
y' = [12x + 10y * y'] / (6x^2+5y^2)
y' - [(10y y') / (6x^2+5y^2)] = 12x / (6x^2+5y^2)
y'(1 - 10y / (6x^2+5y^2) = 12x / (6x^2+5y^2)
y'[(6x^2+5y^2-10y) / (6x^2+5y^2)] = 12x / (6x^2+5y^2)
y' = 12x / (6x^2+5y^2-10y)