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Higher order derivatives. Higher order differentials. Extrema of multivariable functions
1. Lecture 3
Higher order derivatives. Higherorder differentials. Extrema of
multivariable functions
2. Higher order derivatives
f ( x, y )Mixed derivatives
f ( x, y )
x
2 f ( x, y )
x 2
Example 3.1
2 f ( x, y )
x y
f ( x, y )
y
2 f ( x, y )
y x
2 f ( x, y )
y 2
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6. Higher order derivatives for compositions of functions
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9. Higher order differentials
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11. Differential of k-order
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13. Higher order differentials for composition of function
Differential for the caseof independent variables
Expressions for differentiating of
differentials dx1 and so on
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Differentials of higher orders formultivariable function are not invariant.
15. Extrema of multivariable function. Necessary conditon.
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Necessary condition of extremaor