Derivatives in Parametric Form: Find Curve Slope Problem
First Derivative in Parametric Form
Second Derivative in Parametric Form
EXAMPLES:
"Find the slope of the curve x= e^θ sinθ, y= e^θ cosθ; when θ=π/3."
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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