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Partial Differentiation

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Instructor: Niraj Singh

Language: English/Hindi

A partial derivative of a function that depends on more than one variables is its derivative with respect to one of those variables, with the others held constant (as different to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry.

The partial derivative of a function  {\displaystyle f(x,y,\dots )} with respect to the variable x is variously denoted by 

{\displaystyle f'_{x},f_{x},\partial _{x}f,\ D_{x}f,D_{1}f,{\frac {\partial }{\partial x}}f,{\text{ or }}{\frac {\partial f}{\partial x}}.}

This chapter is further divided into the following 2 classes:

  • Class A: Evaluating Single and Higher-order Partial Derivatives using Chain rule

  • Class B: Evaluating Single and Higher-order Partial Derivatives of Composite Functions
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