#### To determine

**To find:** The derivative of the function f(x).

#### Answer

The derivative of the function f(x)=5.2x+2.3 is 5.2.

#### Explanation

**Given:**

The function f(x)=5.2x+2.3.

**Formula used:**

**Derivative of a Constant Function:**

If *c* is a constant function, then ddx(c)=0 (1)

**The Constant Multiple Rule:**

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

ddx[c⋅f(x)]=c⋅ddxf(x) (2)

**The Power Rule:**

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

ddx(xn)=nxn−1 (3)

**The Sum Rule:**

If f(x) and g(x) are both differentiable functions, then the sum rule is,

ddx[f(x)+g(x)]=ddx(f(x))+ddx(g(x)) (4)

**Calculation:**

The derivative of f(x)=5.2x+2.3 is f′(x) is as follows

f′(x)=ddx(f(x)) =ddx(5.2x+2.3)

Apply the sum rule as shown in equation (4).

f′(x)= ddx(5.2x)+ddx(2.3)

Apply the constant multiple rule as shown in equation (2).

f′(x)=5.2ddx(x)+ddx(2.3)=5.2ddx(x1)+ddx(2.3)

Apply the power rule as shown in equation (3)

f′(x)=5.2(1x1−1)+0=5.2(1x0)+0=5.2(1)+0=5.2

Therefore, the derivative of the function f(x)=5.2x+2.3 is 5.2.