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derivabbrev-diff-exp-integrate-true

diff (x *exp ((x)), x...

derivabbrev: true;

'integrate (f(x, y),...

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derivabbrev-diff-exp-integrate-true

diff (exp ((x)), x, .2);

derivabbrev: true;

'integrate (f(x, y),...

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derivabbrev-integrate-true

derivabbrev: true;

integrate (1/P^2, P);

eq1: % = C;

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derivabbrev-diff-integrate-true

'diff (a*x^2+b*x, x, 1);

diff(%o1,x);

derivabbrev: true;

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derivabbrev-diff-integrate-true

diff (a*x^2+b*x, x, 1);

derivabbrev: true;

'integrate (f(x, y),...

Calculate

derivabbrev-diff-exp-integrate-true

diff (x *exp ((x)), x...

derivabbrev: true;

'integrate (f(x, y),...

Calculate

derivabbrev-diff-log-sin-true

diff ((log(sin(5*x)))...

derivabbrev: true;

Calculate

derivabbrev-diff-sin-true

diff((sin(a-x))^2, x,...

derivabbrev: true;

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derivabbrev-diff-exp-integrate-true

diff (exp (f(x)), x, m);

derivabbrev: true;

'integrate (f(x, y),...

Calculate

derivabbrev-diff-exp-true

diff (exp (f(x)), x, 2);

derivabbrev: true;

diff (%, x);

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derivabbrev

Run Example
```(%i1)derivabbrev:true ;
(%o1)                                true
(%i2) mainvar: t;
(%o2)                                  t
(%i3) x(t):= r(t)*sin(theta(t));
(%o3)                     x(t) := r(t) sin(theta(t))
(%i4) y(t):=r(t)*cos(theta(t));
(%o4)                     y(t) := r(t) cos(theta(t))
(%i5) xdot(t):= diff(x(t), t, 1);
(%o5)                     xdot(t) := diff(x(t), t, 1)
(%i6) ydot(t):= diff(y(t), t, 1);
(%o6)                     ydot(t) := diff(y(t), t, 1)
(%i7) xdotdot(t):= diff(xdot(t), t, 1);
(%o7)                  xdotdot(t) := diff(xdot(t), t, 1)
(%i8) ydotdot(t):= diff(ydot(t), t, 1);
(%o8)                  ydotdot(t) := diff(ydot(t), t, 1)
(%i9) thetadot(t):= diff(theta(t), t, 1);
(%o9)                 thetadot(t) := diff(theta(t), t, 1)
(%i11) Assumption1: xdotdot(t)=0;
2
(%o11) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
t t                               t
+ 2 r(t)  cos(theta(t)) theta(t)  + r(t)    sin(theta(t)) = 0
t                       t       t t
(%i12) solve(Assumption1, r(t));
sin(theta(t)) r(t)    + 2 cos(theta(t)) theta(t)  r(t)
t t                           t     t
(%o12) [r(t) = - -------------------------------------------------------]
2
cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
t t                          t
(%i13) Assumption2: ydotdot(t)=0;
2
(%o13) - r(t) sin(theta(t)) theta(t)    - r(t) cos(theta(t)) (theta(t) )
t t                               t
- 2 r(t)  sin(theta(t)) theta(t)  + r(t)    cos(theta(t)) = 0
t                       t       t t
(%i14) E1_1: subst(rdot(t), diff(r(t), t, 1), Assumption1);
2
(%o14) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
t t                               t
+ 2 rdot(t) cos(theta(t)) theta(t)  + r(t)    sin(theta(t)) = 0
t       t t
(%i15) E1_2: subst(rdotdot(t), diff(diff(r(t), t, 1),t,1), E1_1);
2
(%o15) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
t t                               t
+ 2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t)) = 0
t
(%i16) E1_3: subst(rr(t), r(t), E1_2);
2
(%o16) rr(t) cos(theta(t)) theta(t)    - rr(t) sin(theta(t)) (theta(t) )
t t                                t
+ 2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t)) = 0
t
(%i17) E1_4: solve(E1_3, rr(t));
2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t))
t
(%o17) [rr(t) = - ------------------------------------------------------------]
2
cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
t t                          t
(%i18) E1_5: subst(r(t), rr(t), E1_4[1]);
2 rdot(t) cos(theta(t)) theta(t)  + rdotdot(t) sin(theta(t))
t
(%o18) r(t) = - ------------------------------------------------------------
2
cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
t t                          t
(%i19) ```
Run Example
```derivabbrev:true ;
(%o1)                                true
(%i2) x(t):= r(t)*sin(theta(t));
(%o2)                     x(t) := r(t) sin(theta(t))
(%i3) y(t):=r(t)*cos(theta(t));
(%o3)                     y(t) := r(t) cos(theta(t))
(%i4) xdot: diff(x(t), t, 1);
(%o4)         r(t) cos(theta(t)) theta(t)  + r(t)  sin(theta(t))
t       t
(%i5) ydot: diff(y(t), t, 1);
(%o5)         r(t)  cos(theta(t)) - r(t) sin(theta(t)) theta(t)
t                                            t
(%i6) xdotdot: diff(xdot, t, 1);
2
(%o6) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
t t                               t
+ 2 r(t)  cos(theta(t)) theta(t)  + r(t)    sin(theta(t))
t                       t       t t
(%i7) ydotdot: diff(ydot, t, 1);
2
(%o7) - r(t) sin(theta(t)) theta(t)    - r(t) cos(theta(t)) (theta(t) )
t t                               t
- 2 r(t)  sin(theta(t)) theta(t)  + r(t)    cos(theta(t))
t                       t       t t
(%i8) Assumption1: xdotdot=0;
2
(%o8) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
t t                               t
+ 2 r(t)  cos(theta(t)) theta(t)  + r(t)    sin(theta(t)) = 0
t                       t       t t
(%i9) Assumption2: ydotdot=0;
2
(%o9) - r(t) sin(theta(t)) theta(t)    - r(t) cos(theta(t)) (theta(t) )
t t                               t
- 2 r(t)  sin(theta(t)) theta(t)  + r(t)    cos(theta(t)) = 0
t                       t       t t
(%i10) E1: solve(Assumption1, r(t));
sin(theta(t)) r(t)    + 2 cos(theta(t)) theta(t)  r(t)
t t                           t     t
(%o10) [r(t) = - -------------------------------------------------------]
2
cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
t t                          t
(%i11) E2: solve(Assumption2, r(t));
cos(theta(t)) r(t)    - 2 sin(theta(t)) theta(t)  r(t)
t t                           t     t
(%o11) [r(t) = -------------------------------------------------------]
2
sin(theta(t)) theta(t)    + cos(theta(t)) (theta(t) )
t t                          t
(%i12) solve(subst(E2, [E1]), r(t));
(%o12)                                []
(%i13) E3: solve(lhs(E1)-lhs(E2), r(t));
3
2 (theta(t) )  r(t)
t       t
(%o13)                [r(t)    = - --------------------]
t t         theta(t)
t t
(%i14) ```
Run Example
```diff (a*x^y+b*x, x, 1);
y - 1
(%o1)                           a x      y + b
(%i2) diff(%,x);
(%o2)                                  0
(%i3)  derivabbrev: true;
(%o3)                                true
(%i4)  'integrate (f(x, y), y, g(x), h(x));
h(x)
/
[
(%o4)                          I     f(x, y) dy
]
/
g(x)
(%i5)  diff (%, x);
(%o5)                                  0
(%i6) ```

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