Question

The area of a square with side s is A(s)=s2. What is the rate of change of the area of a square with respect to its side length when s=10?

Answer 1

Answer:

$\dfrac{dA}{ds}=20$

Step-by-step explanation:

Given that,

The area of a square is given by :

A = s² ....(1)

Where

s is the side of the square.

Differentiating (1) wrt s.

$\dfrac{dA}{ds}=\dfrac{d}{ds}(s^2)\\\\\dfrac{dA}{ds}=2s$

Put s = 10 in the above equation.

$\dfrac{dA}{ds}=2\times 10\\\\=20\ units$

So, the rate of change of the area of a square is 20 units