Question

Find the differential of the function w = 3xyexz?

Answer 1

To find the differential of the function w = 3xyexz, take the partial derivatives with respect to x, y, and z and combine them with the differentials of x, y, and z.

Step-by-step explanation:

To find the differential of the function w = 3xyexz, we need to use the rules of differentiation. Here's the step-by-step process:

1. Start with the function w = 3xyexz.
2. Take the partial derivative of w with respect to x, treating y and z as constants: ∂w/∂x = (3yexz).
3. Take the partial derivative of w with respect to y, treating x and z as constants: ∂w/∂y = (3xexz).
4. Take the partial derivative of w with respect to z, treating x and y as constants: ∂w/∂z = (3xyexz).

So, the differential of the function w = 3xyexz is: dw = (3yexz)dx + (3xexz)dy + (3xyexz)dz.