Log and Exponential Functions

Differentiation and Integration

>	with(plots):

Warning, the name changecoords has been redefined

>	diff(ln(x),x);

>	diff(ln(-x),x);

>	diff(ln(a*x),x);

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

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

>	diff(log10(x),x);

>	diff(log[5](x),x);

>	diff(log[3](x^2+2*x),x);

>	LnGraph:=plot(ln(x),x=-8..8,y=-8..8,thickness=2):

>	ExpGraph:=plot(exp(x),x=-8..8,y=-8..8,thickness=2,color=green):

>	LineGraph:=plot(x,x=-8..8,y=-8..8,thickness=2,color=blue):

>	display(LnGraph,ExpGraph,LineGraph);

>	diff(exp(x),x);

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

>	diff(4^x,x);

Note above that the answer represents  times .

>	diff(exp(2*sin(x)),x);

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

>

value(%);

>	Int((2*x+3)/(x^2+3*x),x=1..2);

>

value(%);

>

evalf(%);

>	plot((2*x+3)/(x^2+3*x),x=1..2,filled=true);

>	plot(1/x,x=4..10,filled=true);

>	int(4*x*exp(x^2),x=2..4);

>

evalf(%);

>	plot(4*x*exp(x^2),x=2..4,filled=true);

>	plot(2*exp(x),x=4..16,filled=true);

>	diff(4^(x^2),x);

>	Diff(log[4]((x^2+3)/4),x);

>

value(%);

>	Diff(ln((x^2+3)/4)/ln(4),x);

>

value(%);

>	int((5*x^2)/(x^3+3),x);

>	int((2*x)/(x^2+3),x=0..2);

>	plot((2*x)/(x^2+3),x=0..2,filled=true);

>	plot(1/x,x=3..7,filled=true);

>	Int(28*exp(4*x),x=0..1);

>

value(%);

>

evalf(%);

>	plot(28*exp(4*x),x=0..1,filled=true);

>