Question Sheet 5 - Challenge Problem Example Answers

1. Search the helpfile for the TimeUsed[ ] command. Use this to determine how much longer Mathematica takes to compute  (d/dx)2x using ‘==’ compared with the command Dt[ ].

(Hint: use TimeUsed[ ], before and after using both commands.)

2. In the screencast we introduced the Dt[ ] command. Search the helpfile for the D[ ] command. What is the difference between the Dt[ ] and D[ ] command?

3. Calculate (∂_x)(∂_y)sin(2x)sin(y).
 [Note that the notation (∂_x), is equivalent to (∂/(∂x)).]

4. Calculate ((∂_x)^2)((∂_y)^2)sin(2x)sin(y).
 [Note that similarly to above, the notation ((∂_x)^2), is equivalent to ((∂^2)/(∂(x^2))).]