Exercises
Best give a name to everything, and make sure that the input (original
formula) is echoed on the screen to check for correct typing. Choose
your favorite name for the derivative.
Pay attention to upper/lower case, :+ versus =, and the semicolon at the end.
| > | y:=x^3+3*x^2-1; dydx:=diff(y,x); |
Careful about parentheses. sqrt is more common than ^(1/2).
Either one is VERY different from ^0.5 which you should avoid.
| > | y:=1/sqrt(x)-x^(1/3); dydx:=diff(y,x); |
e is just the letter e -- the exponential function is denoted exp. Its value
exp(1) at 1 is Euler's number.
| > | y:=exp(x)-x^(exp(1)); dydx:=diff(y,x); |
MAPLE does not know a quotient rule -- instead it rewrites p/q as p*q^(-1)
and uses product and chain rule. Same result -- different appearnce.
| > | y:=(x^23+3*x)/(x^3-5*x+1); dydx:=diff(y,x); simplify(dydx); |
MAPLE automatically simplifies double fractions
| > | y:= (3*x^2-4*x+5) / ( x / (6*x^4-12) ); dydx:=diff(y,x); simplify(dydx); |
Parentheses and *
| > | y:=(2+sin(3*x))/(2+cos(3*x)); dydx:=diff(y,x); simplify(dydx); |
Parentheses
| > | y:=sin(x^2); dydx:=diff(y,x); |
parentheses
| > | y:=(sin(x))^2;; dydx:=diff(y,x); |
same as above -- but MAPLE allows one to omit outher pair of parnetheses.
| > | y:=sin(x)^2; dydx:=diff(y,x); |
inverse function is different from 1/function or negative exponent!
| > | y:=3*arcsin(5*x); dydx:=diff(y,x); |
To learn which functions MA{PLE knows -- and what MAPLE calss them -- e.g.
arcsin, asin or ....? one reasonabl;e tsart is to ask for help for
| > | ?functions |
and then scroll to bottom of the page. There you will find a link to inifcns -- which may
also be reached directly if you remember that name. Scrolling far down that page you
will find MAPLE's names for the inverse trig functions....
| > | ?inifcns |
| > | y:=7/sin(x); dydx:=diff(y,x); |
Same again -- using negative exponents
| > | y:=7*sin(x)^(-1); dydx:=diff(y,x); |
| > | y:=2*x+11*arctan(3*x); dydx:=diff(y,x); |
| > | y:=x*ln(x)+4; dydx:=diff(y,x); |
In modern math log means ln, log w/ base 10 is 19th century
| > | y:=x*log(x)+4; dydx:=diff(y,x); |
| > | y:=x*(log(x)+4);; dydx:=diff(y,x); |
| > | y:=(x-1)*log(x); dydx:=diff(y,x); |
Note how the 6 disappears!!!!!!!! Chain rule
| > | y:=log(6*x); dydx:=diff(y,x); |
Alternative explanation: expand the logarithm! log(6) is just an additive constant!
| > | expand(y); |
| > | y:=(x^2-sqrt(x))/x-3;; dydx:=diff(y,x); simplify(dydx); |
many parentheses
| > | y:=sin((x^(1/3)-x^(1/4))/(3*x-7)); dydx:=diff(y,x); simplify(dydx); |
| > |