Question

What is the gradient of this function:

Z=(2 x+3 y) eʸ
All Variables are restricted to the domain on which the function is defined.

Answer 1

The gradient of the function Z = (2x + 3y)e^y is (2e^y, (2x + 3y)e^y + 3e^y).

Step-by-step explanation:

The gradient of the function Z = (2x + 3y)e^y can be found by taking the partial derivative with respect to x and y. Let's find the partial derivative with respect to x first:

∂Z/∂x = 2e^y

Next, let's find the partial derivative with respect to y:

∂Z/∂y = (2x + 3y)e^y + 3e^y

Therefore, the gradient of the function is (∂Z/∂x, ∂Z/∂y) = (2e^y, (2x + 3y)e^y + 3e^y).