Question

Find dy/dx by implicit differentiation.
4x2 + 5xy - y2 = 6

Answer 1

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)

Answer 2

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