Question

use implicit differentiation to find dy/dx - 2xy-y^2= 1 can someone explain step by step with formulas explaining in detail.

Answer 1

Let me call dy/dx y'

Answer 2

use product rule for -2xy and power rule for -y^2:

-2x*y' + y*(-2) - 2y*y' = 0

Answer 3

-2xy' - 2y - 2yy' = 0, divide everything by -2:
xy' + y + yy' = 0

Answer 4

now move y to the right side:
xy' + yy' = -y

Answer 5

you lost the =1

Answer 6

where?

Answer 7

-2xy-y^2 = 1 is original problem right?

Answer 8

yeah, but derivative of a constant is 0!

Answer 9

gotcha

Answer 10

what is the formula for implicit differentiation
?

Answer 11

now move y to the right side:
xy' + yy' = -y
take y' out:
y'(x+y) = -y

Answer 12

there is no formula, u use a combination of several formulas

Answer 13

oh ah...ok let me look and little by little look into what u wrote to understand

Answer 14

y' = dy/dx = -y/(x+y).
Fan me if I helped, thanx! =)