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