LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTA== JSFH JSFH
<Text-field style="Heading 1" layout="Heading 1">Functional Derivative</Text-field> Defining a functional L with respect to two functions of the time, 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, QyQ+SSJMRzYiKiYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2Iy1JInhHRiU2I0kidEdGJSIiIy1GKDYjLUkieUdGJUYvIiIiISIi print(); # input placeholder it is required to derive L with respect to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tRiw2I1EhRidGPQ== and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== . Reply While the normal definition of the derivative fails to perform the request LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElZGlmZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRIkxGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRInhGJ0YvRjItRjY2JC1GIzYjLUYsNiVRInRGJ0YvRjJGQUZB LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= %; Error, invalid input: diff received x(t), which is not valid for its 2nd argument and enables only a full derivative with respect to the independant variable t , QyQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkSSJMRzYiSSJ0R0YoIiIi LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LCYqKi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLUkieEdGKTYjSSJ0R0YpIiIiLUYlNiMtSSJ5R0YpRi1GLy1JJGNvc0dGJkYqRi8tSSVkaWZmR0YnNiRGK0YuRi8iIiMqKEYkRjktRjVGMUYvLUY3NiRGMkYuRi9GLw== In the Physics package the definition of the derivative has been changed to enable the task. It is possible to address the command directly, without loading the pakage LSZJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0klZGlmZkdGJjYkSSJMR0YoLUkieEdGKDYjSSJ0R0Yo LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCQqKC1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLUkieEdGKTYjSSJ0R0YpIiIiLUYlNiMtSSJ5R0YpRi1GLy1JJGNvc0dGJkYqRi8iIiM= LV9JKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiJJJWRpZmZHRiY2JEkiTEdGKC1JInlHRig2I0kidEdGKA== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder KiYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy1JInhHRig2I0kidEdGKCIiIy1JJGNvc0dGJTYjLUkieUdGKEYsIiIi JSFH Alternately, one may load the package QyQtSSV3aXRoRzYiNiNJKFBoeXNpY3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiUiIiI= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder 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 and use the derivatives LUklZGlmZkclKnByb3RlY3RlZEc2JEkiTEc2Ii1JInhHRic2I0kidEdGJw== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCQqKC1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLUkieEdGKTYjSSJ0R0YpIiIiLUYlNiMtSSJ5R0YpRi1GLy1JJGNvc0dGJkYqRi8iIiM= JSFH JSFH
<Text-field style="Heading 2" layout="Heading 2">Further Discussion</Text-field> In the context of the above discussion, it is also recommended to look at the command Fundiff for Functional Differentiation Exampli gratia, Let S, QyQ+SSJTRzYiLUkkSW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQsJiokLUklZGlmZkdGKTYkLUkicUdGJTYjSSR0YXVHRiVGNCIiIyMiIiJGNSomSSJrR0YlRjdGMUY1IyEiIkY1L0Y0OywkSSlpbmZpbml0eUdGKUY7Rj9GOw== print(); # input placeholder derive S with respect to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GLDYlUSYmdGF1O0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0Y9LUkjbW9HRiQ2LVEiLkYnRj0vJSZmZW5jZUdGPC8lKnNlcGFyYXRvckdGPC8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTRj0= JSFH JSFH LUkoRnVuZGlmZkc2IjYkSSJTR0YkLUkicUdGJDYjSSJ0R0Yk LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCYqJkkia0c2IiIiIi1JInFHRiU2I0kidEdGJUYmISIiLUklZGlmZkclKnByb3RlY3RlZEc2JC1GLTYkRidGKkYqRis= JSFH JSFH
JSFH JSFH
JSFH JSFH JSFH JSFH