253
Hosilani hisoblash funksiyasi –
diff.
S ifodadan hosilalarni simvolli hisoblash uchun
diff funksiyasidan
diff(S, x, n)
formatda foydalaniladi.
Aytaylik
y=x
2
sinx funksiyaning birinchi va uchinchi tartibli hosilalarini olish
zarur bo`lsin:
syms x
y=x^2*sin(x);
diff(y,x)
ans=
x^2*cos(x)+2*x*sin(x)
diff(y,x,3)
ans =
6*cos(x)-x^2*cos(x)-6*x*sin(x)
Algebraik
tenglamalarni yechish – solve
Algebraic tenlamalar sistemalarini va yakka tenglamalarni yechish uchun
solve yoki
fzero komanda(buyruq)lari ishlatiladi.
Solve komandasi
Solve(expr1, expr2,…, exprN, var1, var2,…varN) formatda
ishlatiladi va
expr tengliklar
bajariladigan var o`zgaruvchilarning qiymatlari
qaytariladi.
X
3
-1=0 tenglamani yechishni ko`raylik.
syms x
y=x^3-1;
s=solve(y,x)
s=
1
(3^(1/2)*i)/2-1/2
-(3^(1/2)*i)/2-1/2
Differensiallash.
Simvolli ifodalarni defferensallashxamda sonli shakilda ( masalan m fayil
ko’rinishida ) berilgan funksiyalarning xosilasini
aniqlashda diff komandasidan
foydaliniladi.Masalan
ifodaning x bo’yicha differensali
3
+2x+1 bo’ladi.
>> sums x; diff(x^3+x^2+x+2)
ans=
3*x^2+2*x+1
Xuddi shu natijani boshqa yo’l bilan xam olishimiz mumkin :
>>f=inline(‘x^3+x^2+2’)
f=
254
Inline function:
f(x)=x^3+x^2+x+2
>>diff(f(x))
ans=
3*x^2+2*x+1
Ikkinchi xosila uchun sintaksis diff(f(x),2) va n-xosila uchun diff (f(x),n)
kurinishga ega buladi. Yuqorida keltrilgan funksiya uchun ikkinchi, uchunchi va
turtinchi xosilalarni olishni kuraylik:
>>syms x;diff(x^3+x^2+x+2.2)
ans=
6*x+2
>>syms x;diff(x^3+x^2+x+2.3)
ans=
6
>>syms x;diff(x^3+x^2+x+2.4)
ans=
0
Bir necha uzgarivchilarga ega bo`lgan ifodalarni
xususiy xosilalarini xam
diff
kamandasi yordamida olish mumkin masalan cos
)ifodaning x,y,z
bo`yicha xususiy
xosilalarini mos ravishda
-
, -
, -
ga teng:
>>syms x y z
>>diff(cos(x*y/z)x)
ans=
-sin(x*y/z)*y/z
>>diff(cos(x*y/z))
ans=
-sin(x*y/z)*x*y/z^2
Xar hil o`zgarivchilarga nisbatan bir necha xususiy xosilalarni olish uchun
diff kamandasi kup marta ishlatilishi kerak, masalan cos
) ifodani avval x kiyin
y va undan kiyin z bo’yicha xususiy xosilasi quydagicha olinadi:
>>syms x z y
>>diff(diff(diff(cos(x*y/),x,)y,)z,)
ans=
-sin(x*y/z)*x^2*y^2/z^4+3*cos(x*y/z)*x/z^3*y+sin(x*y/z)z^2
