Differentiate the function.
S(R) = 4πR^2
To differentiate the function S(R) = 4πR^2, we can follow the steps below:
Step 1: Identify the variable with respect to which you want to differentiate the function. In this case, the variable is R.
Step 2: Apply the power rule of differentiation. The power rule states that to differentiate a term with the form x^n, you multiply the exponent by the coefficient and reduce the exponent by 1.
For our function S(R) = 4πR^2, the coefficient is 4π, and the exponent is 2. Applying the power rule, we differentiate the function as follows:
dS/dR = 2 * 4πR^(2-1)
= 8πR^1
= 8πR
Therefore, the derivative of the function S(R) = 4πR^2 with respect to R is dS/dR = 8πR.
To differentiate the function S(R) = 4πR^2, you can use the power rule of differentiation. The power rule states that if you have a function of the form f(x) = x^n, where n is a constant, then the derivative of f(x) with respect to x is given by df(x)/dx = n*x^(n-1).
In this case, S(R) = 4πR^2. To differentiate this function, we need to find the derivative dS/dR.
Applying the power rule, we can differentiate each term separately:
- For the term 4π, the derivative is 0, because it is a constant.
- For the term R^2, the derivative with respect to R is 2R.
Therefore, the derivative of S(R) = 4πR^2 with respect to R is:
dS/dR = 2(4πR) = 8πR.
So, the derivative of S(R) is 8πR.