Some Differentiation Examples 
From Class

For those of you who wish to use Mathematica, here are today’s class examples on taking partials of different functions. Link to the Mathematica introduction is my website > Multi > Days > Into Mathematica. Feel abundantly free to come to office hours to ask more questions.

The general structure is SO easy! Below is the second example we did on the board for finding the first order partials. (Remember, you need either to use “Enter” on an extended keyboard or push “Enter + Shift” to get Mathematica to evaluate your code.)

D[x^y,x]

D[x^y,y]

Here are the 2nd order partials. Also, I use the Simplify[%] command. “Simplify” is, I hope, self-explanatory. The % means “put in the last output.” (Unfortunately, it won’t change (-2 + y) to (y - 2)! Why? Because Stephen Wolfram hates me.) 

Sometimes the bar below an output offers “Simplify” as an option; then one need only click it.

There’s also an example of how to use the “take multiple derivatives of the same variable” command, D[f(x,y), {y, 2}].

D[x^y,x,x]

Simplify[%]

D[x^y,{y,2}]

Here are the mixed 2nd order partials:

D[x^y,x,y]

Simplify[%]

D[x^y,y,x]

Simplify[(x^(-1+y))+(x^(-1+y)) y Log[x]]