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Mathematics 62 Online
OpenStudy (anonymous):

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

OpenStudy (bahrom7893):

Let me call dy/dx y'

OpenStudy (bahrom7893):

use product rule for -2xy and power rule for -y^2: -2x*y' + y*(-2) - 2y*y' = 0

OpenStudy (bahrom7893):

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

OpenStudy (bahrom7893):

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

OpenStudy (anonymous):

you lost the =1

OpenStudy (bahrom7893):

where?

OpenStudy (anonymous):

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

OpenStudy (bahrom7893):

yeah, but derivative of a constant is 0!

OpenStudy (anonymous):

gotcha

OpenStudy (anonymous):

what is the formula for implicit differentiation ?

OpenStudy (bahrom7893):

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

OpenStudy (bahrom7893):

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

OpenStudy (anonymous):

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

OpenStudy (bahrom7893):

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

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