Partial Derivatives Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Determine the partial derivatives and given

(2) Determine the partial derivatives and given

(3) Determine the partial derivatives and given (a) and (b)

(4) Determine the partial derivatives and given

(5) Determine the partial derivatives and given

(6) Determine the partial derivatives and given   

(7) Determine the partial derivatives and given   

(8) Determine the partial derivatives and by differentiating implicitly  given    

(9) Determine the partial derivatives and by differentiating implicitly  given with and     

(10) Compute the slope of the tangent line to the graph of the function at the point in the direction of the -plane and of the -plane.

(11) Determine the partial derivatives and given

(12) Show that the function is harmonic on the -plane with the point removed.

(13) For show that the mixed partial derivatives are identical:

(14) For show that the mixed partial derivatives are identical:

(15) Determine where   

(16) Determine and given

      and       .  

(17) Determine and by differentiating implicitly given   

     and     

(18) Show that but does not exist, where

.

(19) The heat equation is , and the wave equation is show which of the following satisfies these equations:

(20) The Cauchy-Riemann equations are   and where and are functions of and Show which of the following satisfies these equations:  

    (a)     (b)

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