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- https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/59%3A__Partial_Derivatives/59.01%3A_First_Partial_Derivativesthen how do we take the derivative of f ? In this case, there are two possible first derivatives: one with respect to x, and one with respect to y. For example, if \(g(x, y)=3 x^{4} y^{7}\...then how do we take the derivative of f ? In this case, there are two possible first derivatives: one with respect to x, and one with respect to y. For example, if g(x,y)=3x4y7, then the partial derivative of g with respect to x is ∂g/∂x=12x3y7, since both 3 and y7 are considered constants with respect to x.
- https://phys.libretexts.org/Bookshelves/University_Physics/Radically_Modern_Introductory_Physics_Text_I_(Raymond)/08%3A_Geometrical_Optics_and_Newtons_Laws/8.05%3A_Math_Tutorial__Partial_DerivativesIn order to understand the generalization of Newtonian mechanics to two and three dimensions, we first need to understand a new type of derivative called the partial derivative. It is just like an ord...In order to understand the generalization of Newtonian mechanics to two and three dimensions, we first need to understand a new type of derivative called the partial derivative. It is just like an ordinary derivative, except that when taking the derivative of the function with respect to one of the variables, the other variables are held constant. Note that a special symbol “ ∂” is used in place of the normal “d” for the partial derivative.
- https://phys.libretexts.org/Bookshelves/Mathematical_Physics_and_Pedagogy/Complex_Methods_for_the_Sciences_(Chong)/02%3A_Derivatives/2.04%3A_Partial_DerivativesFunctions can also take multiple inputs; for instance, a function f(x,y) maps two input numbers, x and y , and outputs a number. In general, the inputs are allowed to vary independently of one an...Functions can also take multiple inputs; for instance, a function f(x,y) maps two input numbers, x and y , and outputs a number. In general, the inputs are allowed to vary independently of one another. The partial derivative of such a function is its derivative with respect to one of its inputs, keeping the others fixed.
