Derivatives in Parametric Form: Differential Calculus Problem#6

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DERIVATIVE IN PARAMETRIC FORM:

First Derivative in Parametric Form
Second Derivative in Parametric Form

EXAMPLES:

Find the dy/dx and d²y/dx² of the given functions.

1. x= t³+1 ; y= t²+1

2. x= t^-3 ; y= t³ + 3t

3. x= u³ + 1; y= 4u²-4u

4. x= √(u+2) ; y= u²-3

5. x= 1+ cos t ; y= sin²t

6. x= 1-lnt ; y= t-lnt

7. x= cosθ + θsinθ ; y= sinθ - θ cosθ

8. x= cos³θ ; y= sin³θ

9. x= e^Ø ; y= 2e^-Ø

10. x= Øe^Ø ; y= e^Ø

11. Find the slope of the cycloid x=a(θ-sinθ) , y=a(1-cosθ); when θ=π/2.

12. Find the slope of the curve x= e^θ sinθ, y= e^θ cosθ; when θ=π/3.

13. Find the equation of the tangent to the curve x = 2sint, y= cos2t; when t= π/6.

14. Find the equation of the tangent to the curve x =lnt, y= t^-1; when t = 2.

______________________________

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