The area of a square with a side s is A(s)=s^2.What is the rate of the change of the area of a square in respect to its side?
dA/ds = 2 s
Draw a picture and you will see why
To find the rate of change of the area of a square with respect to its side, we need to differentiate the area function A(s) = s^2 with respect to s.
To differentiate s^2, we can use the power rule of differentiation. According to the power rule, if we have a function f(x) = x^n, then the derivative of f(x) with respect to x is given by f'(x) = n*x^(n-1).
Applying the power rule to our case, where A(s) = s^2, we have:
A'(s) = 2*s^(2-1) = 2*s
Thus, the rate of change of the area of a square with respect to its side is given by the derivative A'(s) = 2*s.