August 31st, 2015, 05:03 AM  #1 
Newbie Joined: Aug 2015 From: Egypt Posts: 1 Thanks: 0  Implicit Function
I tried to solve these ones, but ended up with some weird results ... so any help? 1st one: x^(2)*(y^2 + 1) = 5 Prove that: x^3 y dy/dx + 5 = 0 !! 2nd : y = sqrt(1 + sqrt(x + sqrt(x))) Prove that: dy/dx = (2 sqrt(x) + 1)/(8y (y^2  1) sqrt(x)) and last one ... Find the angle between the target of the curve x^2 + 3xy + y^2 = 5 at point (1,1) Last edited by skipjack; August 31st, 2015 at 07:25 AM. 
August 31st, 2015, 07:22 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,962 Thanks: 1606 
1st one: differentiating gives x²(2y dy/dx) + 2x(y² + 1) = 0. Multiplying that by x/2 gives x³y dy/dx + x²(y² + 1) = 0, and the desired result follows. Hint for 2nd one: show that (y²  1)² = x + √x, then differentiate. What does "the angle between the target of the curve" mean? 

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derviative, function, implicit 
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