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Subsections
The purpose of this lab is to calculate derivatives using the diff command and the D command in Maple.
Maple knows how to take many derivatives. Its main commands for doing this are D and diff. D is designed to differentiate functions, whereas diff is for differentiating expressions. However, if proper notation is used, diff can also be used with functions. To review the difference between a function and an expression, see the two examples below. The statement defines a function, the statement defines an expression.
> f:=x>x^23*x+1;
> g:=x^2+5*x2;
Here are some examples that show how D and diff work for the function and the expression .
> D(f);
> D(f)(x);
> diff(f(x),x);
> diff(g,x);
Note that the output for D(f) is the only one above that has an arrow in it. This means that if you assign the output of D(f) to a label, the derivative can be used as a function in Maple whereas all other outputs when given a label would have to be used as expressions. The examples below show how this works for and .
> df := D(f);
> df(1);
> df2 := D(f)(x);
> subs(x=1, df2);
> df3 := diff(f(x),x);
> subs(x=1, df3);
The D command and the diff command do not require the function or expression to be entered first. Here are some other examples of how these commands can be used.
> D(sin);
> D(sin)(x);
> D(sin)(Pi/2);
> diff(cos(x),x);
Finding the equation of a tangent line to a function at a given point can be done using the pointslope form of a line.
Where and .
This can be done rather easily in Maple and we can even plot and the tangent line on the same graph. See how this can be done for the tangent line to
at .
> f := x> sqrt(x^2x+1);
> y_tan := f(1) + D(f)(1)*(x1);
> plot({f(x),y_tan}, x=0..2);
 Compute the derivatives of the following functions using both the diff command and the D operator for each function.


 Find the equation of the tangent line to
at the point where . Include a plot of the function and the tangent line on the same graph.
 Find all points on the graph of
where the slope is equal to 1. Don't forget that a point includes both the and coordinates.
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Dina Solitro
20011127