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Shukla, and Fatemeh YarahmadiMelissa HallingCover PageyesTOC OnlyCompile but don't publishLicensePublic DomainCC BYCC BY-SACC BY-NC-SACC BY-NDCC BY-NC-NDGNU GPLAll Rights ReservedCC BY-NCGNU FDLCK-12Show Page TOCyesnoTranscludedyesPrintOptionsNo Header/FooterNo TitleNo Header/Footer/TitleOER program or PublisherCollege of the Canyons - Zero Textbook Cost ProgramASCCC OERI ProgramCK-12OpenStaxGALILEOOpenSUNYMIT OpenCourseWareVirginia Tech Libraries' Open Education InitiativeThe Publisher Who Must Not Be NamedeCampusOntarioWAC ClearinghouseBC CampusLumenOpen OregonOpenStax CNXPDXOpenEvergreen Valley CollegeAutonumber Section Headingstitle with space delimiterstitle with colon delimiterstitle with dash delimitersLicense Version1.02.02.53.04.01.31.2Print CSSDefaultDenseVirginia TechScreen CSSDefaultVirginia TechCosmologyNumber of Print ColumnsTwoThreeInclude attachmentsContent TypeDocumentImageOther Searching inAll resultsAbout 1 results1.3: Derivativeshttps://math.libretexts.org/Bookshelves/Analysis/Tasty_Bits_of_Several_Complex_Variables_(Lebl)/01%3A_Holomorphic_Functions_in_Several_Variables/1.03%3A_DerivativesUsing the standard chain rule, \[\begin{align}\begin{aligned} \frac{\partial}{\partial z_j} \left[ g \circ f \right] & = \frac{1}{2} \left( \frac{\partial}{\partial x_j} - i \frac{\partial}{\partial y...Using the standard chain rule, \[\begin{align}\begin{aligned} \frac{\partial}{\partial z_j} \left[ g \circ f \right] & = \frac{1}{2} \left( \frac{\partial}{\partial x_j} - i \frac{\partial}{\partial y_j} \right) \left[ g \circ f \right] \\ & = \frac{1}{2} \sum_{\ell=1}^m \left( \frac{\partial g}{\partial s_\ell} \frac{\partial u_\ell}{\partial x_j} + \frac{\partial g}{\partial t_\ell} \frac{\partial v_\ell}{\partial x_j} - i \left( \frac{\partial g}{\partial s_\ell} \frac{\partial u_\ell}{\part…MoreShow more results
