Find dy/dx by implicit differentiation.

4x2 + 5xy - y2 = 6

Hello,

Method 1:

z=f (x, y) = 4x²+5xy-y²-6=0

z'=8x+5y+5xy'-2yy'=0

y' (5x-2y) = - (8x+5y)

y' = - (8x+5y) / (5x-2y)

Method 2:

@f/@x=8x+5y

@f/@y=5x-2y

dy/dx = - (@f/@x) / (@f/@y) = - (8x+5y) / (5x-2y)

So the question ask to find dy/dx by implicit differentiation of 4x^2 + 5xy - y2=6, and base on my further calculation and further computation about the said question, I would say that the answer would be dy/dx = (8x+5y) / (2y-5x). I hope you are satisfied with my answer and feel free to ask for more