Logarithms 

The natural logarithm is defined as the ln command. 

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

 

>	value(%) assuming x>0;

 

>	diff( ln(x), x );

 

>	plot( ln(x), x=0..5 );

 

General logarithms can be found with log, giving the base of the log in a special way. 

>	log[10](x);

 

>	plot( [ log[2](x), ln(x), log[4](x) ], x=0..5, color=[red,green,blue] );

 

Exponentials 

General exponentials are written using the caret ^ for exponential notation. 

>

2^x;

 

>	diff( 10^x, x );

 

For the natural (base-e) exponential, however, it's better to use the function exp instead. In fact, the number e is not defined. 

>

exp(x);

 

>

e^x;

 

If you look carefully, you will see that the two previous results are a little different (the font of the e). 

>	diff( exp(x), x );

 

>	diff( e^x, x );

 

You are free to define e and then use the caret form, but it's easy to forget the defintion step and get confusing results. 

>	e:= exp(1);

 

>	diff( e^x, x );

 

Inverse trig functions 

We do not use the "-1" notation for inverse functions in Maple. The inverse trig functions all have names beginning with arc. 

>	arccos(0);

 

>	diff( arctan(x), x );

 

>	csc( arctan(x) );

 

Hyperbolic functions 

All the hyperbolic functions are defined as you would expect. 

>	int( sinh(x), x);

 

>	limit( tanh(x), x=infinity );

 

>	plot( [cosh(x),sinh(x),tanh(x)], x=-2..2, color=[red,black,blue] );