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Diff(exp(x^2), x):%=value(%);
Diff(exp(x^2), x$2):%=value(%);
alias(y=y(x));
eq:=x^2+y^2=c;
dydx:=solve(diff(eq,x), diff(y,x));
alias(y=y);
Diff(exp(a*x*y^2), x,y$2): %=value(%);
Integrate(x/(x^3+1),x): %=value(%);
Integrate(x/(x^3+1),x=1..2): %=value(%);
Sum(k^7, k=1..20): %=value(%);
t:=taylor(sin(tan(x))-tan(sin(x)), x=0, 13);
Limit((x^2-1)/(2*x^2-x-1),x=1): %=value(%);
Limit( cos(x)^(1/x^3), x=0, right): %=value(%);
d i f f ( e^x^2 ,x)
2 xe(x2
)
d i f f ( e^x^2 ,x , 2 )
4 x2
e(x2
) + 2 e(x2
)
y=function ( 'y') (x) ; dy=y . d i f f (x) ; dy
∂
∂x
y (x)
var ( 'c')
c
eq=x^2+y^2==c ; eq
x2
+ y (x)2
= c
solve ( eq . d i f f (x) ,dy)
[
∂
∂x
y (x) = −
x
y (x)
]
r e s e t () ; var ( 'y , a , k')
(y, a)
d i f f ( e ^(a*x*y^2) ,x ,1 , y , 2 )
4 a3
x2
y4
e(axy2
) + 10 a2
xy2
e(axy2
) + 2 ae(axy2
)
i n t e g r a te (x/(x^3+1) ,x)
1
3
√
3 arctan
(
1
3
√
3(2 x − 1)
)
+
1
6
log
(
x2
− x + 1
)
−
1
3
log (x + 1)
i n t e g r a te (x/(x^3+1) ,x , 1 , 2 )
1
18
√
3π −
1
6
log (3) +
1
3
log (2)
sum(k^7 ,k ,1 ,20)
3877286700
taylor ( sin ( tan (x) ) - tan ( sin (x) ) ,x ,0 ,11)
−
1913
75600
x11
−
29
756
x9
−
1
30
x7
l i m i t (( x^2 -1) /(2*x^2 -x -1) ,x=1)
2
3
l i m i t ( cos (x) ^(1/x^3) , x=0, dir='+')
0