Obtain the derivative of 𝑧=(2𝑥-𝑦)(𝑥+3𝑦) with respect to y

To find the derivative of the function z=(2x-y)(x+3y) with respect to y, we will use the product rule. The product rule states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.

Let's denote: f = 2x - y g = x + 3y

We need to find the derivatives of f and g with respect to y: df/dy = -1 dg/dy = 3

Now, we can apply the product rule: dz/dy = f * (dg/dy) + g * (df/dy) dz/dy = (2x - y) * 3 + (x + 3y) * (-1) dz/dy = 6x - 3y - x - 3y dz/dy = 5x - 6y

So, the derivative of z=(2x-y)(x+3y) with respect to y is dz/dy = 5x - 6y.