Theorem of implicit functions help

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SUMMARY

The discussion centers on applying the theorem of implicit functions to calculate derivatives in a calculus problem involving parametric equations. Specifically, the user seeks to find dy/dx and d²y/dx² at θ=π/2 for the equations x=a(θ-sinθ) and y=a(θ+sinθ). The solution involves first determining dy/dθ and dx/dθ, then using the relationship dy/dx=(dy/dθ)/(dx/dθ) to derive the necessary derivatives. Additionally, the user is tasked with finding a formula for d²x/dy² in terms of dy/dx and d²y/dx², and verifying this formula for the function y=x².

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  • Understanding of parametric equations in calculus
  • Familiarity with the theorem of implicit functions
  • Knowledge of differentiation techniques
  • Ability to work with second derivatives
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  • Practice calculating derivatives of parametric equations
  • Learn how to derive second derivatives from first derivatives
  • Explore verification techniques for calculus formulas using specific functions
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Students studying calculus, mathematics educators, and anyone interested in advanced differentiation techniques and implicit function theory.

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hi guys,
im a little stuck at the moment trying to answer the follwing calculus question, can anyone help me please.

if x=a(theta-sintheta), y=a(theta+sintheta), find dy/dx and d^2y/dx^2 at the point where theta=pi/2.

and given that dy.dx=(dx/dy)^-1, find a fomula for d^2x/dy^2 in terms of dy/dx and d^2y/dx^2.
and verify the formula for y=x^2

i really don't know where to start with this one. :cry: :frown: :rolleyes:
 
Last edited:
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Do you know the theorem of implicit functions...?

Daniel.
 
you have to first get the dy/d(theta) and dx/d(theta) and then place them like
dy/d(theta) *d(theta)/dx =dy/dx
 

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