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The Maxima on-line user's manual

Algebra Calculator

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Diff Calculator

Diff

Function: diff (<expr>, <x_1>, <n_1>, ..., <x_m>, <n_m>)

plot2d ([cos(x),cos(x)^2,/*sin(x)^2,*/cos(x)-cos(x)^2], [x,0,2*%pi]);
i:A*sin(2500*t);
v:diff(i,t)*L;
integrate(v,t);

Function: diff (<expr>, <x>, <n>)

Function: diff (<expr>, <x>)

Function: diff (<expr>) Returns the derivative or differential of <expr> with respect to some or all variables in <expr>.

diff (<expr>, <x>, <n>) returns the <n>th derivative of <expr> with respect to <x>.

diff (<expr>, <x_1>, <n_1>, ..., <x_m>, <n_m>) returns the mixed partial derivative of <expr> with respect to <x_1>, ..., <x_m>. It is equivalent to diff (... (diff (<expr>, <x_m>, <n_m>) ...), <x_1>, <n_1>).

diff (<expr>, <x>) returns the first derivative of <expr> with respect to the variable <x>.

diff (<expr>) returns the total differential of <expr>, that is, the sum of the derivatives of <expr> with respect to each its variables times the differential del of each variable. No further simplification of del is offered.

The noun form of diff is required in some contexts, such as stating a differential equation. In these cases, diff may be quoted (as diff) to yield the noun form instead of carrying out the differentiation.

When derivabbrev is true, derivatives are displayed as subscripts. Otherwise, derivatives are displayed in the Leibniz notation, dy/dx.

Examples:

          (%i1) diff (exp (f(x)), x, 2);
                               2
                        f(x)  d               f(x)  d         2
          (%o1)       %e     (--- (f(x))) + %e     (-- (f(x)))
                                2                   dx
                              dx
          (%i2) derivabbrev: true$
          (%i3) integrate (f(x, y), y, g(x), h(x));
                                   h(x)
                                  /
                                  [
          (%o3)                   I     f(x, y) dy
                                  ]
                                  /
                                   g(x)
          (%i4) diff (%, x);
                 h(x)
                /
                [
          (%o4) I     f(x, y)  dy + f(x, h(x)) h(x)  - f(x, g(x)) g(x)
                ]            x                     x                  x
                /
                 g(x)

For the tensor package, the following modifications have been incorporated:

(1) The derivatives of any indexed objects in <expr> will have the variables <x_i> appended as additional arguments. Then all the derivative indices will be sorted.

(2) The <x_i> may be integers from 1 up to the value of the variable dimension [default value: 4]. This will cause the differentiation to be carried out with respect to the <x_i>th member of the list coordinates which should be set to a list of the names of the coordinates, e.g., [x, y, z, t]. If coordinates is bound to an atomic variable, then that variable subscripted by <x_i> will be used for the variable of differentiation. This permits an array of coordinate names or subscripted names like X[1], X[2], ... to be used. If coordinates has not been assigned a value, then the variables will be treated as in (1) above.

There are also some inexact matches for diff. Try ?? diff to see them.

(%o1)                                true
(%i2) 

Diff Example

Related Examples

diff-ode2

diff(v,t,1)+P(x)+Q(x)...

EQ1:diff(v,t,1)=-(-a+...

ode2(EQ1,v,t);

Calculate

diff

diff(ln(c/(a+b*x)),x,1);

Calculate

diff-integrate-pi-sqrt

f:2*sqrt(x);

i:integrate((2*sqrt(x...

df:diff:(f,x);

Calculate

diff-ev-numer-solve

q:q1 + q2;

p: 10- q;

g1:p*q1 - q1;

Calculate

diff-exp

diff(t*exp(t),t,n);

Calculate

diff-display2d-expand-false-ratsimp

display2d:false;

x: ax*(1-t)^3 + bx*(1...

ratsimp(expand(diff(x...

Calculate

diff-display2d-facsum-false-ratsimp

display2d:false;

Nst:(He^2+Cs^2)*(a3*C...

Ncs:diff(Nst,Cs);

Calculate

diff

a:x^2-3*y+2;

b:diff(a,x);

Calculate

diff-matrix

f(x,y):=-ln(1+x)-ln(1...

xx:diff(diff(f(x,y),x...

xy:diff(diff(f(x,y),x...

Calculate

diff

f(x,y):=(x^2+y^3)^(1/2);

xx:diff(diff(f(x,y),x...

xy:diff(diff(f(x,y),x...

Calculate