Mit Index und
ist die spaltenweise Ableitung der beiden Funktionen
Die jeweiligen Komponenten des Gradienten werden partiell abgeleitet.
![[image]](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAaCAIAAAAMmCo2AAAAAXNSR0IArs4c6QAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAAIRJREFUOE9j/P//PwMhwERIAUh+oBXd2T7RmtF64h0UtwJ9Bwe3J6RZgSWtJtxGFoc5/M72dGvG+FUMOmBVOmoqmCbdnmCVNmEbSDeQBZRO24Zs0H8GFB4ORQMdTtjicjC6CS0wb29LA7s8DRz8MABVBIpaK0jkIgBQBBI/jMMmjWOLOwApWo9vDHmy9AAAAABJRU5ErkJggg== "embedded image (png)"){kind=small}
und ![[image]](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAaCAIAAAAMmCo2AAAAAXNSR0IArs4c6QAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAAKpJREFUOE/FkrEBhCAMRcWxZB9cR1unuAo2cAQb2CVnEuIhRrnOdITn/z8RAwBdq/oWgPcvQSmFebTWSFk7hnTk3acD7+jofMQTQMyNYeJGJ5A0GMvf5SZBSsVp2LUzdLeCuK3FBnUhDuU836p27CWICpHKaY5aiUSqSc92TPxsJG+hRDZXogyOSG1TKWkImrPw8Vv0x8cQbjx8luf3aVCtVS8938dYf2X6AidfXPxoacJAAAAAAElFTkSuQmCC "embedded image (png)"){kind=small}
und ![[image]](data:image/png;base64,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 "embedded image (png)"){kind=small}
![[image]](data:image/png;base64,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 "embedded image (png)"){kind=small}
ist die spaltenweise Ableitung der beiden Funktionen ![[image]](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAaCAIAAAAMmCo2AAAAAXNSR0IArs4c6QAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAAJlJREFUOE/tks0NwyAMhU3HMvs46yTLkEV6Kuzi+I8EqkpRr1XfBWE+4PlBYma40+MO0PU/9FUEbV9yUuWt9XijtOwA8ixcCKlUrisKQCVKDuvUoC6jcK2yS0fZ55ogPwsRjbw0Q3bEGyHs/MDt9fz4K2ZHSBS2Rq/9OnOjndiF3uEp8Gpv1vIIqhYi9w/OWE4hj2uspZ/+4weAXtdC+XOlTAAAAABJRU5ErkJggg== "embedded image (png)"){kind=small}
und ![[image]](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAaCAIAAADjWkEIAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAALZJREFUOE/tk9sRAyEIRTFluf247WgzphjthQDqCo6ZMf/ha8Xj5XFnHSLCQbwOGEb+3H5RP+2lpvtyHFeqj1xNLefc/aYklhx8LIglejqGTEaOyIFfSQq22Z5kTjQMh/K85/mOz0Nf6a2VCZuPNGcEuV3VrOHmKPylOrD99Zl9zCu1cq2ynabNbuqOJZqKW05tTO170ZMxjCGTBbrkMuzeaptWhNG5QGLRNkDcBx+ajV/DHf7nH+OKuXIwf9oGAAAAAElFTkSuQmCC "embedded image (png)"){kind=small}
![[image]](data:image/png;base64,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 "embedded image (png)"){kind=small}