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: 19,293 Thanks: 1684 
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? 

Tags 
derviative, function, implicit 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
(Implicit function theorem)  uint  Calculus  4  February 19th, 2015 05:36 AM 
implicit function  MATHEMATICIAN  Abstract Algebra  5  February 12th, 2015 09:37 AM 
Implicit function theorem  chess1  Real Analysis  0  April 13th, 2014 10:16 PM 
Implicit Function Theorem  Robert Lownds  Real Analysis  2  June 12th, 2013 12:27 AM 
Second derivatives of implicit function  OriaG  Calculus  2  May 25th, 2013 02:56 PM 