Question

Find the first partial derivatives with respect to x, y, and z and evaluate each at the given point. function point w = xye9z3 4, 5, - 1 3?

Answer 1

To find the first partial derivatives with respect to x, y, and z of the function w = xye^9z^3, differentiate the function with respect to each variable. Then, substitute the given values into the derivatives to evaluate them at the specified point.

Step-by-step explanation:

To find the first partial derivatives with respect to x, y, and z, we need to differentiate the function w = xye^9z^3 with respect to each variable separately.

The first partial derivative with respect to x is y * e^9z^3.

The first partial derivative with respect to y is x * e^9z^3.

The first partial derivative with respect to z is 3 * x * y * e^9z^3.

To evaluate each derivative at the given point (4, 5, -1), substitute x=4, y=5, and z=-1 into the respective derivatives.