Question

Find dy/dx by implicit differentiation.
3x^2 + 5xy - y^2 = 8

Answer 1

implicit differentation:

(d/dx)(3x^2) +(d/dx)(5xy) -(d/dx)(y^2) = (d/dx)(8)

dy/dx = y'

6x + (5xy' + 5y) -2yy' =0

y'(5x -2y) +6x +5y=0

y'(5x -2y) = -6x -5y

y' = (-6x -5y)/(5x -2y)

That should be it :)

Answer 2

thank you!