We've introduced the differential operator before, during a few of our calculus lessons. But now we will be using this operator more and more over the prime symbol we are used to when describing differentiation, as from now on we will frequently be differentiating with respect to a specific variable, and we will have to keep track of which one it is. This leads us to the concept of partial derivatives. Although partial differential equations sound like extremely advanced math, and they will get pretty hairy a little later in the series, they're aren't too daunting when just going over their definitions, so let's see what they are and also learn about the gradient of a function, which involves partial derivatives. Script by Howard Whittle Watch the whole Mathematics playlist: http://bit.ly/ProfDaveMath Classical Physics Tutorials: http://bit.ly/ProfDavePhysics1 Modern Physics Tutorials: http://bit.ly/ProfDavePhysics2 General Chemistry Tutorials: http://bit.ly/ProfDaveGenChem Organic Chemistry Tutorials: http://bit.ly/ProfDaveOrgChem Biochemistry Tutorials: http://bit.ly/ProfDaveBiochem Biology Tutorials: http://bit.ly/ProfDaveBio EMAIL► ProfessorDaveExplains@gmail.com PATREON► http://patreon.com/ProfessorDaveExplains Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience! Amazon: https://amzn.to/2HtNpVH Bookshop: https://bit.ly/39cKADM Barnes and Noble: https://bit.ly/3pUjmrn Book Depository: http://bit.ly/3aOVDlT