The Chain Rule and the Gradient

  • Serge Lang
Part of the Undergraduate Texts in Mathematics book series (UTM)


In this chapter, we prove the chain rule for functions of several variables and give a number of applications. Among them will be several interpretations for the gradient. These form one of the central points of our theory. They show how powerful the tools we have accumulated turn out to be.


Vector Field Unit Vector Differentiable Function Tangent Plane Tangent Line 
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Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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