what is the derivation for the formula of the area of a circle?i would like to know how it is derieved. pl help...
The area of the circle is a function of radius of that circle.
A(r) = `pi` *r^2
We'll calculate the derivative of the area, differentiating with respect to r.
Since `pi` is a constant, we'll differentiate r^2, using the derivative formula:
(x^n)' = n*(x^(n-1))*(x)'
(x^n)' = n*(x^(n-1))*1
(x^n)' = n*(x^(n-1))
Comapring, we'll get:
(r^2)' = 2*(r^(2-1))*(r)'
(r^2)' = 2*r
dA/dr = A'(r) = 2`pi` r (circumference of the circle)
The requested derivative of the area of circle is dA/dr = A'(r) = 2`pi` r.