여러변수가있는표현식의도함수gydF4y2Ba

둘이상의기호변수를포함하는표현식을미분하려면어떤변수에대해미분할지를지정하십시오。그런다음gydF4y2BadiffgydF4y2Ba명령으로해당변수에대한표현식의편도함수를계산합니다。예를들어,다음과같은기호표현식이있다고가정해보겠습니다。gydF4y2Ba

Syms s t f = sin(s*t);gydF4y2Ba

다음명령을실행하면gydF4y2Ba

差异(f, t)gydF4y2Ba

편도함수gydF4y2Ba $$\partial gydF4y2Ba\mathrm{fgydF4y2Ba}/gydF4y2Ba\partial gydF4y2Ba\mathrm{tgydF4y2Ba}$$가계산됩니다。결과는다음과같습니다。gydF4y2Ba

ans = s * cos (s * t)gydF4y2Ba

변수gydF4y2Ba年代gydF4y2Ba에대해gydF4y2BafgydF4y2Ba를미분하려면다음을입력하십시오。gydF4y2Ba

差异(f, s)gydF4y2Ba

이경우다음값이반환됩니다。gydF4y2Ba

ans = t * cos (s * t)gydF4y2Ba

어떤변수에대해미분할지지정하지않으면MATLAB에서디폴트변수를선택합니다。기본적으로디폴트변수는알파벳상에서x에가장가까운문자입니다。gydF4y2Ba디폴트기호변수찾기gydF4y2Ba에서전체규칙을참조하십시오。위의예제에서gydF4y2Ba差异(f)gydF4y2Ba는gydF4y2BatgydF4y2Ba에대해gydF4y2BafgydF4y2Ba의도함수를구합니다。이는문자gydF4y2BatgydF4y2Ba가문자gydF4y2Ba年代gydF4y2Bax에보다알파벳상에서더가깝기때문입니다。어떤변수에대해MATLAB이미분하는지를파악하려면gydF4y2BasymvargydF4y2Ba을사용하십시오。gydF4y2Ba

symvar (f, 1)gydF4y2Ba

ans = tgydF4y2Ba

tgydF4y2Ba에대한gydF4y2BafgydF4y2Ba2계의도함수를계산합니다。gydF4y2Ba

差异(f t 2)gydF4y2Ba

이명령은다음결과를반환합니다。gydF4y2Ba

ans = s ^ 2 * sin (s * t)gydF4y2Ba

tgydF4y2Ba는디폴트변수이므로gydF4y2Ba差异(f, 2)gydF4y2Ba는동일한답을반환합니다。gydF4y2Ba

추가예제gydF4y2Ba

diffgydF4y2Ba명령에대해더자세히알아보려면MATLAB작업공간에서다음을입력하여gydF4y2Ba一个gydF4y2Ba，gydF4y2BabgydF4y2Ba，gydF4y2BaxgydF4y2Ba，gydF4y2BangydF4y2Ba，gydF4y2BatgydF4y2Ba및gydF4y2BaθgydF4y2Ba를정의하십시오。gydF4y2Ba

信谊gydF4y2Ba一个gydF4y2BabgydF4y2BaxgydF4y2BangydF4y2BatgydF4y2BaθgydF4y2Ba

다음표에서는gydF4y2Ba差异(f)gydF4y2Ba를입력한결과를보여줍니다。gydF4y2Ba

符号x n f = x^n;gydF4y2Ba

差异(f)gydF4y2Ba

Ans = n*x^(n - 1)gydF4y2Ba

Syms a b t = sin(a*t + b);gydF4y2Ba

差异(f)gydF4y2Ba

Ans = a*cos(b + a*t)gydF4y2Ba

Syms theta f = exp(i*theta);gydF4y2Ba

差异(f)gydF4y2Ba

ans = exp(我)θ* 1 * 1gydF4y2Ba

zgydF4y2Ba에대해제1종베셀함수gydF4y2Babesselj(ν,z)gydF4y2Ba를미분하려면다음을입력하십시오。gydF4y2Ba

Syms z b = besselj(nu,z);db = diff (b)gydF4y2Ba

이경우다음값이반환됩니다。gydF4y2Ba

Db = (nu*besselj(nu, z))/z - besselj(nu + 1, z)gydF4y2Ba

diffgydF4y2Ba함수는기호행렬을입력값으로받을수도있습니다。이경우,미분은요소별로수행됩니다。다음예제를보겠습니다。gydF4y2Ba

信谊一个x = [cos (x *),罪(* x); sin (x *),因为(a * x))gydF4y2Ba

이경우다음값이반환됩니다。gydF4y2Ba

[-sin(A *x)， cos(A *x)] [-sin(A *x)， cos(A *x)]gydF4y2Ba

다음명령을실행하면gydF4y2Ba

diff (A)gydF4y2Ba

다음결과가반환됩니다。gydF4y2Ba

ans =[——*罪(* x), a * cos (x *)][——* cos (x *),——* sin (x *))gydF4y2Ba

벡터인수에대해벡터함수의미분을수행할수도있습니다。gydF4y2Ba $$\mathrm{xgydF4y2Ba}＝gydF4y2Ba\mathrm{rgydF4y2Ba}\mathrm{因为gydF4y2Ba}\mathrm{\lambda gydF4y2Ba}\mathrm{因为gydF4y2Ba}\mathrm{\phi gydF4y2Ba}$$，gydF4y2Ba $$\mathrm{ygydF4y2Ba}＝gydF4y2Ba\mathrm{rgydF4y2Ba}\mathrm{因为gydF4y2Ba}\mathrm{\lambda gydF4y2Ba}\mathrm{罪gydF4y2Ba}\mathrm{\varphi gydF4y2Ba}$$및gydF4y2Ba $$\mathrm{zgydF4y2Ba}＝gydF4y2Ba\mathrm{rgydF4y2Ba}\mathrm{罪gydF4y2Ba}\mathrm{\lambda gydF4y2Ba}$$로놓고유클리드좌표(x, y, z)를구면좌표gydF4y2Ba $$（gydF4y2Ba\mathrm{rgydF4y2Ba}，gydF4y2Ba\mathrm{\lambda gydF4y2Ba}，gydF4y2Ba\mathrm{\phi gydF4y2Ba}）gydF4y2Ba$$로변환한다고가정해보겠습니다。gydF4y2Ba $$\mathrm{\lambda gydF4y2Ba}$$는고도또는위도에해당하고gydF4y2Ba $$\mathrm{\phi gydF4y2Ba}$$는방위각또는경도를나타냅니다。gydF4y2Ba

이변환의야코비행렬J를계산하려면gydF4y2Ba雅可比矩阵gydF4y2Ba함수를사용하십시오。J의수학표기법은다음과같습니다。gydF4y2Ba

툴박스에서사용되는구문에맞게gydF4y2Ba $$\mathrm{\lambda gydF4y2Ba}$$에는gydF4y2BalgydF4y2Ba을,gydF4y2Ba $$\mathrm{\phi gydF4y2Ba}$$에는gydF4y2BafgydF4y2Ba를사용합니다。다음명령을실행하면gydF4y2Ba

Syms r l f x = r*cos(l)*cos(f);y = r * cos (l) * sin (f);z = r * sin (l);J =雅可比矩阵([x;y;[r l f])gydF4y2Ba

다음야코비행렬이반환됩니다。gydF4y2Ba

J = [cos (f) * cos (l) - r * cos (f) * sin (l) - r * cos (l) * sin (f)] [cos (l) * sin (f) - r * sin (f) *罪(l), r * cos (f) * cos (l)][罪(l), r * cos (l), 0]gydF4y2Ba

또한다음명령을실행하면gydF4y2Ba

detJ =简化(依据(J))gydF4y2Ba

다음결과가반환됩니다。gydF4y2Ba

detJ = - r ^ 2 * cos(左)gydF4y2Ba

雅可比矩阵gydF4y2Ba함수의인수는열벡터또는행벡터가될수있습니다。또한야코비행렬의행렬식은다소복잡한삼각함수표현식이기때문에gydF4y2Ba简化gydF4y2Ba를사용하여삼각함수대입및축약(단순화)을수행할수있습니다。gydF4y2Ba

다음표에는gydF4y2BadiffgydF4y2Ba및gydF4y2Ba雅可比矩阵gydF4y2Ba이간단히요약되어있습니다。gydF4y2Ba