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Implicit Differentiation (2nd Derivative)

Find d^2y/dx^2 given

x^2 + y^2 = 1

Thanks! :smile:

x² + y² = 1
2x + 2y(dy/dx) = 0
dy/dx = -2x/(2y)
dy/dx = -x/y

d²y/dx² = d/dx(-x/y)
= d/dx(-xy^-1)
= -y^-1 + xy^-2(dy/dx)
= -y^-1 + xy^-2(-x/y)
= -y^-1 - x²y^-3

Reply 2

devesh254

The answer I have got here is -1/y^3 :confused:

...any idea why that is? could the textbook be wrong?

Reply 3

yazan_l

x^2 + y^2 = 1
x² = 1-y²

d²y/dx² = -y^-1 - x²y^-3
d²y/dx² = -y^-1 - (1-y²)y^-3
d²y/dx² = -y^-1 - y^-3 + y^-1
d²y/dx² = - y^-3

Edit: i continued e-unit's work...

Reply 4

RichE

Both answers are right if you recall that x^2+y^2=1 at any point on the curve

Reply 5

devesh254

1) x² = 1-y²

2) d²y/dx² = -y-1 - x2y-3

Can u please elaborate on how u went from the line 1 to line 2?

Thanks!

Reply 6

yazan_l

Edit:
oh u were talking to me! hehe..
well i didnt get the second line from the first one... i just put them so as to use them... that's why i left a space between them...