SOLUTION: Would really appreciate help with the following question on my task sheet. Find dy=dx as a function of x and y when: (a) y - x sin y - 3x^2 - 1 = 0 and (ii) x^2y^3 - x

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Would really appreciate help with the following question on my task sheet. Find dy=dx as a function of x and y when: (a) y - x sin y - 3x^2 - 1 = 0 and (ii) x^2y^3 - x      Log On


   

Question 375002: Would really appreciate help with the following question on my task sheet.

Find dy=dx as a function of x and y when:
(a) y - x sin y - 3x^2 - 1 = 0
and
(ii) x^2y^3 - x^2 + 3y - 3 = 0
Finally
(c) (1 - x^2) tan^-1 y = 3
Need to brush up on these, have looked in engineering mathmatics book, having difficulty, and the instructor isnt really approachable
Thanks
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use implicit differentiation,
dy-x%2Acos%28y%29dy-sin%28y%29dx-6xdx=0
dy%281-x%2Acos%28y%29%29=%28sin%28y%29%2B6x%29dx
dy%2Fdx=%286x%2Bsin%28y%29%29%2F%281-x%2Acos%28y%29%29
Do the remaining problems similarly.
Repost if you get stuck.