jagomart
digital resources
picture1_Differentiation Pdf 170718 | Partials


 151x       Filetype PDF       File size 0.04 MB       Source: www.sfu.ca


File: Differentiation Pdf 170718 | Partials
partial differentiation for functions of more than one variable f f x y take area as an example a xy for an increase xx in a yx y constant 1 ...

icon picture PDF Filetype PDF | Posted on 26 Jan 2023 | 2 years ago
Partial capture of text on file.
                     Kenyon College                                                              paquind@kenyon.edu
                                                             Math 333
                                      Some Practice with Partial Derivatives
                     Suppose that f(t,y) is a function of both t and y. The partial derivative of f with
                     respect to y, written
                                                                   ∂f,
                                                                   ∂y
                     is the derivative of f with respect to y with t held constant. To find ∂f, you should
                                                                                                     ∂y
                     consider t as a constant and then find the derivative of f with respect to y.
                                                        2      3
                     Example. Suppose f(t,y) = t sin(y ). Then
                                                         ∂f      2       3     2
                                                         ∂y =t cos(y )·3y .
                     Some Practice Problems.
                                                3 2         ∂f
                       1. Suppose f(t,y) = t y . Find ∂y.
                                                 t+y        ∂f
                       2. Suppose f(t,y) = e        . Find ∂y.
                                                    2           ∂f
                       3. Suppose f(t,y) = ln(t y). Find ∂y.
                       4. Suppose f(t,y) = cos(ty). Find ∂f.
                                                                ∂y
                       5. Suppose f(t,y) =         ty    . Find ∂f.
                                                    3  2
                                                sin(t +y )       ∂y
                     Answers to the Practice Problems.
                           ∂f      3
                       1. ∂y = 2t y
                           ∂f     t+y
                       2. ∂y = e
                           ∂f     1    2
                       3.     = 2 ·t
                           ∂y    t y
                       4. ∂f = −sin(ty)·(t)
                           ∂y
                                       3   2
                       5. ∂f = t−cos(t +y )2y
                           ∂y        2 3   2
                                   sin (t +y )
                     Math 333: Diff Eq                               1                              Partial Derivatives
The words contained in this file might help you see if this file matches what you are looking for:

...Partial differentiation for functions of more than one variable f x y take area as an example a xy increase xx in yx constant yy simultaneous aa the limits da dx dy total differential real single value function two independent variables fx fxy lim paul percival chem spring derivative relations consider z so zz dz derivatives can be taken any order zx taking inverse xz to find third zy yz xyz chain rule and thermodynamics from generalized equation state closed system fp vt six written pt pv tp vvt p pvtpvt but given three inverses e g tv pp v pvt there are only basic properties matter by convention these chosen coefficient thermal expansion isobaric...

no reviews yet
Please Login to review.