For the scalar function T = e − r / 5 cos ⁡ ϕ , determine its directional derivative along the radial direction r ^ and then evaluate it at P ( 2 , π / 4.3 ).

Question

For the scalar function   T  =      e          −      r              /            5        cos  ⁡  ϕ , determine its directional derivative along the radial direction             r      ^       and then evaluate it at   P  (  2  ,  π      /    4.3  ).

Rihanna Robles · Accepted Answer

▽  (      e          −              r        5              cos  ⁡  (  ϕ  )  )  =  (                    −                  e                                    r              5                                      cos        ⁡        (        ϕ        )                    −                  e                                    r              5                                      sin        ⁡        (        ϕ        )                    r      0        ). Evaluated at   P  (  2  ,  π      /    4  ,  3  )  =  (  −  1      /    5  ,  −  1      /    2.  0  )  1      /    (      2        e                  2        5              )

For the scalar function T=e^(-r/5)cos phi, determine its directional derivative along the radial direction hat(r) and then evaluate it at P(2, pi/4.3)

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