Maple Tutor Part 9

Maple Tutor

Part 9: Differentiation

From now on in this tutorial (if you have not been doing it all along), remember to check your inputs by switching to Standard Math mode. That is, click on the x button in the tool bar at the top of the screen. Make sure the input looks like correct mathematics before trying to evaluate it.

Define g to be the function given by

g(x) = x²cos x.
Check your work by evaluating g(pi). You should obtain -pi². If you have trouble, look at Part 7 again.
Now enter
diff(g(x),x);
Then enter
diff(g(x),x,x);
How would you calculate the third derivative?
If you want to calculate the derivative of an expression that you have not yet entered, just replace g(x) by the expression. For example, enter
diff(x^3-x^2+2,x);
Now insert a literal constant in the expression: Enter
diff(x^3-a*x^2+2,x);
Then change the final x to an a. That is, enter
diff(x^3-a*x^2+2,a);
What is the role of the symbol after the comma in the differentiation expression?
Now suppose you want the function dg/dx, that is, g'(x). If necessary, restore the definition of g by entering
g:=x->x²cos(x);
Then enter
D(g);
Then
D(D(g));
Evaluate the second derivative of g at 2 by entering
evalf(D(D(g))(2));
Check your understanding so far by using Maple to calculate the second derivative of tan(x⁶-3x+5) at 3/2. (The value is approximately -4521.)

modules at math.duke.edu