MATLAB
diff(func [, var, n])
func ; var ( , ); n () , ( ).
, , diff.
, , :
>> syms a x
>> f=cos(a*x)
f =
cos(a*x)
>> diff(f)
ans =
-a*sin(a*x)
:
>> syms x y n
>> y=x^n
y =
x^n
>> diff(y,x)
ans =
n*x^(n - 1)
:
>> syms a b t
>> y=sin(a*t+b)
y =
sin(b + a*t)
>> diff(y,t)
ans =
a*cos(b + a*t)
:
>> syms a x
>> f=cos(a*x)
f =
cos(a*x)
>> diff(f,a)
ans =
-x*sin(a*x)
:
>> diff(f,2)
ans =
-a^2*cos(a*x)
>> diff(f,a,2)
ans =
-x^2*cos(a*x)
:
>> diff('tan(x)',x,4)
ans =
16*tan(x)*(tan(x)^2 + 1)^2 + 8*tan(x)^3*(tan(x)^2 + 1)
.
:
>> syms x y
>> diff('y^2/3-x^2/5-1',x)
ans =
-(2*x)/5
>> diff('y^2/3-x^2/5-1',y)
ans =
(2*y)/3
:
>> diff('sin(x)-ln(y)',x,2)
ans =
-sin(x)
>> diff('sin(x)-ln(y)',y,2)
ans =
1/y^2
, . , , , , :
>> syms t
>> x=sym('3*cos(t)^3')
x =
3*cos(t)^3
>> y=sym('3*sin(t)^3')
y =
3*sin(t)^3
>> diff(y)/diff(x)
ans =
-sin(t)/cos(t)
.
:
>> A=[cos(a*x) sin(a*x); -sin(a*x) cos(a*x)]
A =
[ cos(a*x), sin(a*x)]
[ -sin(a*x), cos(a*x)]
>> diff(A)
ans =
[ -a*sin(a*x), a*cos(a*x)]
[ -a*cos(a*x), -a*sin(a*x)]
subs, .
.
[99,103,113,187,190,221]. MATLAB :
limit(func [, x, b, options])
func ; x ; b ( ).
|
|
limit .
.
:
>> syms x h
>> limit((cos(x+h)-cos(x))/h,h,0)
ans =
-sin(x)
limit(func,x,a) func x, a.
.
:
>> syms x n
>> limit((1+x/n)^n,n,inf)
ans =
exp(x)
limit(func,x,inf) func x, .
.
:
>> syms x
>> limit(1/(2-x),x,2)
ans =
NaN
, NaN ans , .
.
:
>> syms x
>> limit(1/(2-x),x,2,'left')
ans =
Inf
>> limit(1/(2-x),x,2,'right')
ans =
-Inf
limit(func,x,a,right) func x, a (.. x , a). limit(func,x,a,left) func x, a (.. x , a).
:
.
:
>> syms x
>> f=2^(1/(x^2-4))
f =
2^(1/(x^2 - 4))
>> limit(f,x,2,'left')
ans =
>> limit(f,x,2,'right')
ans =
Inf