Posted by Angela on Monday, October 8, 2012 at 3:34pm.
using implicit differentiation,
(xy'+y)/√(1+x^2y^2) = 8/3 * 1/(1+16x^2)
a little rearranging of terms yields
y' = 8√(1+x^2y^2) / (3x(1+16x^2)) - y/x
oops that's 1-x^2y^2 throughout
when I plug in the ordered pair (.25, 2)I get a zero in the denominator, was I doing that wrong?
√(1-x^2y^2) = 0, all right, but it's not in the denominator.
So, all you end up with is -y/x = -16
oops: -2/.25 = -8
Rats! I keep being inconsistent in the squaring! √(1-x^2y^2) is not zero.
at (1/4,2)
y' = 8√(1-1/4)/(3*1/4*2) - 2/.25
= (8√6)/3 - 8
judging from my other posts, you'd better double-check this one too!
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