### Related

Calculate

##### taylor

f(x):=1/(1+x);

taylor(f(x),x,0,4);

Calculate

##### diff-solve

f(x):=x^2;

fp(x):=diff(f(x),x);

fp(x);

Calculate

##### diff

diff(%e^(-1/x),x);

diff(1/x,x);

Calculate

f(x):=(sqrt(4*x-2));

draw2d(yaxis =true,ya...

Calculate

draw2d(vector([0,0],[...

Calculate

##### diff-ratsimp

f(x):=(1-x^2)/(1+x^2);

ff(x):=diff( f(x), x,...

ratsimp(ff(x));

Calculate

##### diff-inf-sum-true

sum(t^n/n! * diff(dif...

Calculate

[eq1: y=3*x^2-6*x-1, ...

eqns: [eq1,eq2];

Calculate

draw2d(nticks=1000,ke...

Calculate

Run Example
```(%i1)load(draw);
(%o1)            /usr/share/maxima/5.21.1/share/draw/draw.lisp
(%i2) f:(x-1)^3/((x-2)*x^2);
3
(x - 1)
(%o2)                             ----------
2
(x - 2) x
(%i3) factor(diff(f,x));
2
(x - 4) (x - 1)
(%o3)                          ----------------
2  3
(x - 2)  x
(%i4) factor(diff(f,x,2));
3      2
2 (x - 1) (x  - 8 x  + 16 x - 12)
(%o4)                 - ---------------------------------
3  4
(x - 2)  x
(%i5) subst(3,x,f);
8
(%o5)                                  -
9
(%i6) taylor(f,x,1,10);
3          4            5            6            7
(%o6)/T/ - (x - 1)  + (x - 1)  - 2 (x - 1)  + 2 (x - 1)  - 3 (x - 1)
8            9            10
+ 3 (x - 1)  - 4 (x - 1)  + 4 (x - 1)   + . . .
(%i7) integrate (f,x,3,4);
15 log(3) - 34   10 log(4) - 2 log(2) - 31
(%o7)             -------------- - -------------------------
12                     8
(%i8) integrate (f,x);
5 log(x)   log(x - 2)        1
(%o8)                  - -------- + ---------- + x - ---
4           4            2 x
(%i9) example(draw2d);
(%o9)                                done
(%i10) draw2d(explicit(f,x,3,4));
plotplot2d (f,[x,3,4]);
plot```
Run Example
```load(draw);
(%o1)            /usr/share/maxima/5.21.1/share/draw/draw.lisp
(%i2) f:(x-1)^3/((x-2)*x^2);
3
(x - 1)
(%o2)                             ----------
2
(x - 2) x
(%i3) factor(diff(f,x));
2
(x - 4) (x - 1)
(%o3)                          ----------------
2  3
(x - 2)  x
(%i4) factor(diff(f,x,2));
3      2
2 (x - 1) (x  - 8 x  + 16 x - 12)
(%o4)                 - ---------------------------------
3  4
(x - 2)  x
(%i5) subst(3,x,f);
8
(%o5)                                  -
9
(%i6) taylor(f,x,1,10);
3          4            5            6            7
(%o6)/T/ - (x - 1)  + (x - 1)  - 2 (x - 1)  + 2 (x - 1)  - 3 (x - 1)
8            9            10
+ 3 (x - 1)  - 4 (x - 1)  + 4 (x - 1)   + . . .
(%i7) integrate (f,x,3,4);
15 log(3) - 34   10 log(4) - 2 log(2) - 31
(%o7)             -------------- - -------------------------
12                     8
(%i8) integrate (f,x);
5 log(x)   log(x - 2)        1
(%o8)                  - -------- + ---------- + x - ---
4           4            2 x
(%i9) example(draw2d);
(%o9)                                done
(%i10) draw2d(explicit(f,x,3,4));
plotplot2d (exp(3*s), [s, -2, 2], [logy]);
plot```
Run Example
```load(draw);
(%o1)            /usr/share/maxima/5.21.1/share/draw/draw.lisp
(%i2) f:(x-1)^3/((x-2)*x^2);
3
(x - 1)
(%o2)                             ----------
2
(x - 2) x
(%i3) factor(diff(f,x));
2
(x - 4) (x - 1)
(%o3)                          ----------------
2  3
(x - 2)  x
(%i4) factor(diff(f,x,2));
3      2
2 (x - 1) (x  - 8 x  + 16 x - 12)
(%o4)                 - ---------------------------------
3  4
(x - 2)  x
(%i5) subst(3,x,f);
8
(%o5)                                  -
9
(%i6) taylor(f,x,1,10);
3          4            5            6            7
(%o6)/T/ - (x - 1)  + (x - 1)  - 2 (x - 1)  + 2 (x - 1)  - 3 (x - 1)
8            9            10
+ 3 (x - 1)  - 4 (x - 1)  + 4 (x - 1)   + . . .
(%i7) integrate (f,x,3,4);
15 log(3) - 34   10 log(4) - 2 log(2) - 31
(%o7)             -------------- - -------------------------
12                     8
(%i8) integrate (f,x);
5 log(x)   log(x - 2)        1
(%o8)                  - -------- + ---------- + x - ---
4           4            2 x
(%i9) example(draw2d);