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Sec 15.3 Partial Derivatives

Sec 15.3 Partial Derivatives. Definition: Let f be a function of two variables whose domain includes the point ( a , b ). The partial derivative of f with respect to x at ( a , b ) is defined by

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Sec 15.3 Partial Derivatives

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  1. Sec 15.3 Partial Derivatives Definition: Let f be a function of two variables whose domain includes the point (a, b). The partial derivative of f with respect to x at (a, b) is defined by The partial derivative of f with respect to y at (a, b) is defined by

  2. Definition: If f is a function of two variables , its partial derivatives are the functions: Notation: If z = f (x, y), we write

  3. Definition: If f is a function of three variables , its partial derivatives are the functions:

  4. Higher Derivatives: If z = f (x, y) , its second partial derivatives are the functions:

  5. Clairaut’s Theorem Suppose f is defined on a disk D that contains the point (a, b). If the functions are both continuous on D, then

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