Differentiation and Integration Examples

Use these examples for syntax.

Differentiation Examples

The capital "D" produces a statement of what you want to do and the value(%) computes the derivative.

>	Diff(3*x*sin(4*x^2),x);

>

value(%);

The small "d" computes the derivative immediately.

>	diff(3*x*sin(4*x^2),x);

>	diff((2*x^3-4*x)*(sin(2*x))^2,x);

Here is a second derivative.

>	diff(3*x*sin(4*x^2),x,x);

>	Diff(3*x*sin(4*x^2),x,x);

>

value(%);

In the example below the "a" is treated as a constant.

>	diff(a*x*sin(4*a*x^2),x);

This time the "x" is being treated as a constant.

>	diff(a*x*sin(4*a*x^2),a);

Here is a third derivative.

>	diff(3*x*sin(4*x^2),x,x,x);

You can give a name to the function you wish to differentiate.

>	f:=sin(3*x^2)/(2*x^3+4*x);

>	diff(f,x);

>	poly1:=5*x^4-4*x^3+3*x^2-2*x+1;

>	diff(poly1,x,x);

>	diff(ln(x^2+x),x);

>	diff(ln(x^2+x),x,X);

Note the capital "X" above and the result.  The second differentiation was treated like differentiating a constant.

>	diff(ln(x^2+x),x,x);

>	Diff(exp(x),x);

>	diff(exp(x),x);

>	diff((2*x)^(x^2),x);

Integration Examples

Notice the difference between "Int" and "int".

>	Int(x*sqrt(3*x^2+4),x);

>

value(%);

>	int(x*sqrt(3*x^2+4),x);

Here is a definite integral.

>	Int(x*sqrt(3*x^2+4),x=0..1);

>

value(%);

>	int(x*sqrt(3*x^2+4),x=0..1);

You can use evalf to approximate.

>

evalf(%);

>	Int(x*exp(x^2+2),x);

>	int(x*exp(x^2+2),x);

Note that Maple does not add the arbitrary constant in an indefinite integration.

>	int(1/x,x);

>	Int(1/x,x=1..5);

>	int(1/x,x=1..5);

>	Int(1/x,x=1..5);

>

evalf(%);

>	evalf(ln(5));

>	Int(cos(x^2),x=0..1);

>

evalf(%);

Does the answer above look reasonable from an area interpretation?

>	with(plots):plot(cos(x^2),x=0..1);

>