Question

A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to 18 mm and it wants to know how the area
A(x)
of a wafer changes when the side length x changes. Find
A'(18).

Answer 1

Since we are talking about square wafers, the area is the side length squared
-> A(x) = x^2
Differentiate using power rule: d/dx x^n = n*x^n-1
-> A'(x) = 2x
->A'(18) = 2*18 = 36