> f:=x->x^2+7*x+5; > g:=x^3-5*x+8;Here are some examples that show how

> D(f)(x); > diff(g,x); > diff(f(x),x);See what happens with these.

> diff(g(x),x); > diff(f,x);After the last four examples, you should be convinced that proper notation is very important in doing derivatives in Maple. Maple can also do higher derivatives. Check these commands.

> diff(g,x,x); > (D@@2)(f)(x);If you want to evaluate the derivative at a specific value of

> D(f)(2); > subs(x=3,diff(g,x));Suppose you wanted to find the equation of the tangent line to the graph of

> tanline := D(f)(5)*(x-5)+f(5);More information on

> f:=x^2*y^2+y^3; > implicitdiff(f,y,x);where

> g:=x^2+y^3=1; > implicitdiff(g,y,x);Second derivatives can also be taken with

> implicitdiff(g,y,x,x);Maple also has a command for plotting implicitly defined functions. It is in the package

> with(plots): > implicitplot(x^2-y^2=1,x=-3..3,y=-3..3);

- Find the equation of the line tangent to the graph of the function at . Include a plot of the function and the tangent line on the same graph over the interval .
- Given
, evaluate the third derivative at
using
- the
**D**command. - the
**diff**command.

- the
- Consider the graph defined implicitly by the equation .
- Enter the equation, calling it
*h*. - Use the
**implicitplot**command to verify visually that the graph is an ellipse. - Find the slopes to this curve at the two points where it intersects the x-axis labeling them
*m1*and*m2*. (Hint: You will first need to use the**solve**command to find the y-values) What can you tell about the tangent lines at these points given your answers for the slopes? - Find the equations of the tangent lines to this curve at the two points where it intersects the x-axis labeling them
*t1*and*t2*. Renenber to enter the equations implicitly. - Graph the ellipse and the two tangent lines on one graph.

- Enter the equation, calling it

2004-11-15