Find d 2 y / d x 2 for the curve given by x = 2 cos ⁡ θ a n d y = sin ⁡ θ

Question

Find       d          2        y      /    d      x          2       for the curve given by   x  =  2  cos  ⁡  θ     a  n  d     y  =  sin  ⁡  θ

Hassan Watkins · Accepted Answer

cos  ⁡  (  θ  )  =      x    2    sin  ⁡  (  θ  )  =  y      cos          2        ⁡  (  θ  )  +      sin          2        ⁡  (  θ  )  =  1  ⇒  (      x    2        )          2        +      y          2        =  1  ∴      x          2        +  4      y          2        =  4 [equation of curve]Differentiating both sides with respect to x,  2  x  +  4  ×  (  2  y            d      y              d      x        )  =  0  ∴            d      y              d      x        =  −      x          4      y        ∴      d          d      x        (            d      y              d      x        )  =      d          d      x        (  −      x          4      y        )  ⇒                    d                  2                    y              d              x                  2                      =  −            y      ×      1      −      x      ×                        d          y                          d          x                            4              y                  2                    Now, put value of dy/dx.

Find d^2 y/dx^2 for the curve given by. x=2 cos theta and y=sin theta

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