In Exercises 9-14, find all first and second partial derivatives.
To calculate: The first and second partial derivatives of function
Given Information:
Given function with two variable x, y is
Formula used:
The first partial derivative of
Partial derivative with respect to x, keeping y constant.
Partial derivative with respect to y, keeping x constant
The value of partial derivative at the point
Finding second partial derivative of function
Second partial derivative of
second partial derivatives of
second partial derivatives of
Product rule,
If
Calculation:
Consider the given equation:
Differentiating primary equation
Applying product rule to differentiate above function
Product rule,
If
Then,
Differentiating given equation with respect to y, keeping x as constant
Further simplify,
Hence, first partial derivatives are:
Differentiating
keeping y as constant
Applying product rule to differentiate above function
Product rule,
If
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