Use the product rule to find the derivative of the following function.𝑓(𝑥)=(2𝑥+4)(5𝑥+2)

The product rule for differentiation states that the derivative of the product of two functions is the derivative of the first function times the second function, plus the first function times the derivative of the second function.

Let's denote the first function (2x + 4) as u and the second function (5x + 2) as v.

Step 1: Find the derivative of u, denoted as u'. The derivative of 2x + 4 is 2.

Step 2: Find the derivative of v, denoted as v'. The derivative of 5x + 2 is 5.

Step 3: Apply the product rule. The derivative of the function f(x) = uv is given by f'(x) = u'v + uv'.

Substituting the values we found:

f'(x) = (2)(5x + 2) + (2x + 4)(5) = 10x + 4 + 10x + 20 = 20x + 24

So, the derivative of the function f(x) = (2x + 4)(5x + 2) is f'(x) = 20x + 24.