Question

Consider the following. f(x, y, z) = x2yz − xyz3, p(2, −1, 1), u = 0, 4 5 , − 3 5

Answer 1

The partial derivative of f(x, y, z) with respect to x is 2xyz - yz^3.

Step-by-step explanation:

The question is asking for the partial derivative of the function f(x, y, z) = x^2yz - xyz^3 with respect to x.

To find the partial derivative with respect to x, we keep y and z constant and only differentiate the terms that involve x. Differentiating x^2yz with respect to x gives 2xyz. Differentiating -xyz^3 with respect to x gives -yz^3.

Putting it all together, the partial derivative of f(x, y, z) with respect to x is 2xyz - yz^3.