#### To determine

**To find:** The differentiation of the function S(R)=4πR2.

#### Answer

The differentiation of the function S(R)=4πR2 is 8πR_.

#### Explanation

**Formula used:**

**The Constant Multiple Rule:**

If *c* is a constant and f(x) is a differentiable function, then the constant function rule is,

ddx[c⋅f(x)]=c⋅ddxf(x) (1)

**The Power Rule:**

If n is any real number, then the power rule is,

ddx(xn)=nxn−1 (2)

**Calculation:**

The derivative of S(R)=4πR2 is S′(R) which is computed as follows.

S′(R)=ddR(4πR2)

The value 4π is a real number.

Apply the constant multiple rule as shown in equation (1).

S′(R)=4πddR(R2)

Apply the power rule as shown in equation (2).

S′(R)=4π(2R2−1)=4π(2R1)=8πR

Therefore, the differentiation of the function S(R)=4πR2 is 8πR_.