Question

Find the first partial derivatives of the function f(x, y, z) = 5x sin(y - z)?

Answer 1

The first partial derivatives of the function f(x, y, z) = 5x sin(y - z) are: ∂f/∂x = 5 sin(y - z), ∂f/∂y = 5x cos(y - z), and ∂f/∂z = -5x cos(y - z).

Step-by-step explanation:

To find the first partial derivatives of the function f(x, y, z) = 5x sin(y - z), we need to take the derivative of the function with respect to each variable individually. Let's start with the partial derivative with respect to x:

∂f/∂x = 5 sin(y - z)

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

∂f/∂y = 5x cos(y - z)

Finally, let's calculate the partial derivative with respect to z:

∂f/∂z = -5x cos(y - z)