Search

Loading [MathJax]/jax/output/HTML-CSS/jax.js

Filter Results
Location
- Bookshelves (1)
Classification
- Article type
  - Book or Unit
  - Chapter
  - Section or Page
  - N/A
  - N/A
- Author
  - Jeremy Tatum
  - Lloyd Knox
  - OpenStax
  - Ben Crowell
  - Michael Fowler
  - Paul D'Alessandris
  - Malcolm McMillian
  - Jeffrey W. Schnick
  - Dina Zhabinskaya
  - Chris Impey
  - Douglas Cline
  - Paul Seeburger
  - Tom Weideman
  - Niels Walet
  - David Harrison
  - Boundless
  - Richard Fitzpatrick
  - Fred Jendrzejewski, Selim Jochim, & Matthias Weidemüller
  - Timon Idema
  - Lawrence Davis
  - Daniel Arovas
  - Daniel F. Styer
  - Ryan Martin et al.
  - UCD Physics 7 sans Dina
  - Julio Gea-Banacloche
  - John F. Cochran and Bretislav Heinrich
  - Daniel E. Barth
  - Lei Ma
  - Steven W. Ellingson
  - Michael Richmond
  - David H. Staelin
  - Johan Wevers
  - Peter Dourmashkin
  - Kyle Forinash and Wolfgang Christian
  - Jack C. Straton
  - Graeme Ackland
  - Paola Cappellaro
  - Kim Coble, Kevin McLin, Janelle Bailey, Anne Metevier, Carolyn Peruta, & Lynn Cominsky
  - László Tisza
  - Wolfgang Christian, Mario Belloni, Anne Cox, Melissa H. Dancy, and Aaron Titus, & Thomas M. Colbert
  - David J. Raymond
  - V. Parameswaran Nair
  - Howard Georgi
  - Y. D. Chong
  - Konstantin K. Likharev
  - Evan Halstead
  - Walter Fendt
  - Mihály Benedict
  - Pieter Kok
  - Sander Konijnenberg, Aurèle J.L. Adam, & H. Paul Urbach
  - Edwin F. Taylor & John Archibald Wheeler
  - James M. Fiore
  - Rob Knop
  - Ryan D. Martin, Emma Neary, Joshua Rinaldo, and Olivia Woodman
  - Ronald Kumon
  - Lumen Learning
  - Debra Fischer, Allyson Sheffield, Joshua Tan, and Lily Ling Zhao
- Embed Hypothes.is?
  - yes
- Embebbed CalcPlot3D?
  - yes
- Cover Page
  - yes
  - TOC Only
  - Compile but don't publish
- License
  - Public Domain
  - CC BY
  - CC BY-SA
  - CC BY-NC-SA
  - CC BY-ND
  - CC BY-NC-ND
  - GNU GPL
  - All Rights Reserved
  - CC BY-NC
  - GNU FDL
- Show TOC
  - yes
  - no
- Transcluded
  - yes
- OER program or Publisher
  - College of the Canyons - Zero Textbook Cost Program
  - ASCCC OERI Program
  - CK-12
  - OpenStax
  - GALILEO
  - OpenSUNY
  - MIT OpenCourseWare
  - Virginia Tech Libraries' Open Education Initiative
  - The Publisher Who Must Not Be Named
  - eCampusOntario
  - WAC Clearinghouse
  - BC Campus
  - Lumen
  - Open Oregon
  - OpenStax CNX
  - PDXOpen
  - Evergreen Valley College
- Student Analytics
  - yes
- Autonumber Section Headings
  - title with space delimiters
  - title with colon delimiters
  - title with dash delimiters
- License Version
  - 1.0
  - 2.0
  - 2.5
  - 3.0
  - 4.0
- Print CSS
- Screen CSS
  - default
  - Virginia Tech
  - Cosmology
- PrintOptions
  - No Header/Footer
  - No Title
  - No Header/Footer/Title
Include attachments
- Content Type
  - Document
  - Image
  - Other

2.5: Second Derivatives and Exact Differentials
https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Heat_and_Thermodynamics_(Tatum)/02%3A_Partial_Derivatives/2.05%3A_Second_Derivatives_and_Exact_Differentials
If $z = z(x , y)$ , we can go through the motions of calculating $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ , and we can then further calculate the second derivatives \(...If $z = z(x , y)$ , we can go through the motions of calculating $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ , and we can then further calculate the second derivatives $\frac{\partial ^2 z}{\partial x^2}$ , $\frac{\partial ^2 x}{\partial y^2}$ , $\frac{\partial ^2 z}{\partial y \partial x}$ and $\frac{\partial ^2 z}{\partial y \partial x}$ .

Search

Text Color

Text Size

Margin Size

Font Type

Support Center

How can we help?