Final answer:
To find the partial derivatives of the function g(x, y) = 7x³ + 2y² - 3xy with respect to x and y, we differentiate each term separately. The partial derivative with respect to x is 21x² - 3y, and the partial derivative with respect to y is 4y - 3x. To find 9x at (x, y), substitute the given value of x into the expression 9x.
Step-by-step explanation:
To find the partial derivative of the function g(x, y) = 7x³ + 2y² - 3xy with respect to each of the variables, we differentiate each term separately. For the partial derivative with respect to x, the derivative of 7x³ is 21x², the derivative of 2y² is 0, and the derivative of -3xy is -3y. Thus, the partial derivative of g(x, y) with respect to x is 21x² - 3y.
Similarly, for the partial derivative with respect to y, the derivative of 7x³ is 0, the derivative of 2y² is 4y, and the derivative of -3xy is -3x. Therefore, the partial derivative of g(x, y) with respect to y is 4y - 3x.
Finally, to find 9x at (x, y), substitute the given value of x into the expression 9x. So, 9x at (x, y) is simply 9 multiplied by the given x value.