### Related

##### diff-plot2d-solve

f(x) := (3*x)/(x^2 - ...

f_deriv: diff(f(x), x);

solve (f_deriv=0);

Calculate

##### diff-ic1-ode2

eq: (1+(x^2))*'diff(y...

sol1: ode2(eq,y,x);

sol2: ic1(sol1, x=0,y...

Calculate

##### diff

NOPATtd:(P-COGS)*N;

ROIC:(ROICrail*ICrail...

EVA:IC*(ROIC-WACC);

Calculate

##### diff

'diff(y,x,1)=-(%e^y-5...

Calculate

##### diff-gcd-sqrt

P:4*X^4+8*sqrt(2)*sqr...

PP:16*X^3+8*sqrt(2)*3...

gcd(P,PP);

Calculate

##### diff-exp

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

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

Calculate

##### diff-expand-factor-solve-subst

f:expand(x^2*(x-2*a+2...

factor((solve(diff(f,...

factor((solve(diff(f,...

Calculate

##### diff-exp-factorial-log-min-sum

eq1: (-exp(f)-lambda2...

diff(eq1, f, 1);

Calculate

##### diff

f: (x - xhat)^2 + (y ...

g:(x - p)^2 + (y - q)...

diff(g, a);

Calculate

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

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

Calculate

### diff

Run Example
```(%i1)eq:'diff(y,x,2)+9*y = 9/((cos (3*x))^2);
2
d y             9
(%o1)                        --- + 9 y = ---------
2            2
dx          cos (3 x)
(%i2) ode2(eq, y, x);
sin(3 x) log(sin(3 x) + 1) - sin(3 x) log(sin(3 x) - 1) - 2
(%o2) y = -----------------------------------------------------------
2
+ %k1 sin(3 x) + %k2 cos(3 x)
(%i3) ```
Run Example
```kill(all);
(%o0)                                done
(%i1) Ik:16;
(%o1)                                 16
(%i2) U0:92;
(%o2)                                 92
(%i3) a:I/Ik=1-(U/U0)^2;
2
I         U
(%o3)                            -- = 1 - ----
16       8464
(%i4) l:solve(a,U);
(%o4)            [U = - 23 sqrt(16 - I), U = 23 sqrt(16 - I)]
(%i5) m:solve(a,I);
2
U  - 8464
(%o5)                          [I = - ---------]
529
(%i6) define(I(U),rhs(m[1]));
2
U  - 8464
(%o6)                         I(U) := - ---------
529
(%i7) define(U(I),rhs(l[2]));
(%o7)                       U(I) := 23 sqrt(16 - I)
(%i8) P(I,U):=I*U;
(%o8)                           P(I, U) := I U
(%i9) plot2d(I(U),[U,0,92], [xlabel, "U[V]"], [ylabel, "I[A]"]);
plotplot2d(U(I),[I,0,16], [ylabel, "U[V]"], [xlabel, "I[A]"]);
plotplot2d([P(I(U),U)],[U,0,92], [xlabel, "U[V]"], [ylabel, "P[W]"]);
plotplot2d([P(I,U(I))],[I,0,16], [xlabel, "I[A]"], [ylabel, "P[W]"], [grid, 10, 10]);
plotdefine(Iabgeleitet(U),diff(P(I(U),U),U));
2    2
2 U    U  - 8464
(%o13)               Iabgeleitet(U) := - ---- - ---------
529       529
(%i14) define(Uabgeleitet(I),diff(P(U(I),I),I));
23 I
(%o14)        Uabgeleitet(I) := 23 sqrt(16 - I) - --------------
2 sqrt(16 - I)
(%i15) Umax:solve(Iabgeleitet(U),U);
92           92
(%o15)                   [U = - -------, U = -------]
sqrt(3)      sqrt(3)
(%i16) Imax:solve(Uabgeleitet(I),I);
32
(%o16)                             [I = --]
3
(%i17) P[max]=float(Imax[1]*Umax[2]);
(%o17)                 P    = (I U = 566.5730641647529)
max
(%i18) R[L]=float(Umax[2]/Imax[1]);
U
(%o18)                   R  = (- = 4.979646071760522)
L    I
(%i19) ```
Run Example
```f:z/(1-z);
z
(%o1)                                -----
1 - z
(%i2) g:diff(f,z);
z         1
(%o2)                          -------- + -----
2   1 - z
(1 - z)
(%i3) expand(g);
z           1
(%o3)                        ------------ + -----
2             1 - z
z  - 2 z + 1
(%i4) ```

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