Question

the area of a rectangle is A=lw. Further suppose l=2w. calculate dA in terms of the differential dw.

does this just mean to get the derivative of 2w^2

Answer 1

Yes

Answer 2

well, it means

dA = 4w dw

Answer 3

[AI-generated answer — Explain Bot]

To find the derivative of A = lw with the additional constraint that l = 2w, we need to express A in terms of a single variable, in this case, w.

Given that l = 2w, we can substitute this expression into the area formula A = lw:

A = (2w)(w)
A = 2w^2

Now, we can find the derivative of A with respect to w, using the power rule for derivatives:

dA/dw = d/dw(2w^2)
= 4w

Therefore, dA, which represents the change in A, in terms of the differential dw can be expressed as:

dA = 4w * dw