Question

If f(x, y) = 3x³y³, find f_x(0, 6).

Answer 1

The derivative is 9x²y³, and when evaluated at (0, 6), the result is 0.

Step-by-step explanation:

To find fₓ(0, 6) for the function f(x, y) = 3x³y³, we need to take the partial derivative of f with respect to x and then evaluate it at the given point (0, 6).

First, let's find the partial derivative of f with respect to x. To do this, we treat y as a constant and differentiate each term of the function separately.

The derivative of 3x³y³ with respect to x is 9x²y³.

Now, we substitute the given values x = 0 and y = 6 into the expression we just obtained:

9(0)²(6)³ = 9(0)(216) = 0

Therefore, fₓ(0, 6) is equal to 0.