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Contributed by: Joshua Sabloff and Stephen Wang (Haverford College) (March 2011) Open content licensed under CC BY-NC-SA. As either or varies, you can see how a given partial derivative changes both numerically and graphically. Your current assignment will give you some opportunity to see how this all works. This Demonstration helps students understand what second-order partial derivatives measure.

After finding this I also need to find its value at each point of X( i.e., for X(-1:2/511:+1). diff (F,X)43(1/2)X is giving me the analytical derivative of the function. command twice in a row: D D x3, x, x 6 x The command to compute integrals is Integrate. Mathematica treats all derivatives as partial derivatives, so we have D x y2, x y2 D x y2, y 2 x y To take the second derivative, we can just use the D. What do you mean by 'Can Mathematica graph a double derivative' Can you do that If so, graph y. He has also used a spreadsheet and Mathematica implementations.

with respect to . the students automatically and can calculate partial late credit based on due dates.

Moreover, they are far less easy to understand/interpret, especially if this calculation is just one small piece of a much larger equation (as it often is). But without further simplification (by hand) it will be less efficient, and could potentially exhibit poorer numerical behavior due to the use of a longer sequence of floating-point operations. Longer expressions like these will of course produce the same values. In contrast, here’s the expression produced by taking partial derivatives via Mathematica (even after calling FullSimplify): This formula can be obtained via a simple geometric argument, has a clear geometric meaning, and generally leads to a an efficient and error-free implementation. In particular, if the triangle has vertices \(a,b,c \in \mathbb N \times (b-c). In your homework, you are asked to derive an expression for the gradient of the area of a triangle with respect to one of its vertices.