Find d VC/ d y = ((y/240)^2)(w)

= 2yw/240^2 + 0 + y^2/240^2

but final answer is....

= 2yw/240^2

So, is the question asking for partial derivative or first derivative? I think partial because the final answer only took the derivative with respect to y.

If VC(y)=((y/240)^2)(w)

then VC is not dependent on w, so if you differentiate as a product, the term containing dw/dy drops out (because dw/dy=0), giving you the correct answer.

If w is a function of y, namely w=w(y), then the term dw/dy should be kept:
d(VC)/dy = 2yw/240^2 + y^2/240^2*(dw/dy)

You are correct, the question is asking for the partial derivative with respect to y. In order to find the partial derivative, we need to differentiate the given function with respect to y while treating all other variables (in this case, w) as constants.

Let's break down the steps to find the partial derivative:

1. Start with the given function: VC/y = (y/240)^2 * w

2. To find the partial derivative, we differentiate the function with respect to y. When differentiating a quotient, we can use the quotient rule. Applying the quotient rule to the given function, we get:

d (VC/y)/dy = (2y/240^2) * w

3. Simplify the expression. Since w is a constant, we can bring it out of the derivative:

d (VC/y)/dy = 2yw/240^2

So, the partial derivative with respect to y of VC/y is 2yw/240^2.

It seems that the final answer you provided is the correct solution. The additional terms you included, such as "+ 0" and "+ y^2/240^2," are unnecessary as they evaluate to zero. Therefore, the simplified expression is indeed 2yw/240^2.