The total revenue of selling of x units of a product is represented by `R (x) = 2x^(2)+x+5`.Find its marginal revenue for 5 units.

Explanation

To solve the problem of finding the marginal revenue for selling 5 units of a product, we start with the total revenue function given by:

\[ R(x) = 2x^2 + x + 5 \]

### Step 1: Differentiate the Total Revenue Function
To find the marginal revenue, we need to differentiate the total revenue function \( R(x) \) with respect to \( x \).

\[ R'(x) = \frac{d}{dx}(2x^2 + x + 5) \]

### Step 2: Apply the Power Rule
Using the power rule of differentiation, we differentiate each term:

- The derivative of \( 2x^2 \) is \( 4x \) (using \( \frac{d}{dx}(x^n) = nx^{n-1} \)).
- The derivative of \( x \) is \( 1 \).
- The derivative of the constant \( 5 \) is \( 0 \).

Combining these results, we have:

\[ R'(x) = 4x + 1 \]

### Step 3: Evaluate the Derivative at \( x = 5 \)
Now, we need to find the marginal revenue when \( x = 5 \):

\[ R'(5) = 4(5) + 1 \]

Calculating this gives:

\[ R'(5) = 20 + 1 = 21 \]

### Conclusion
Thus, the marginal revenue for selling 5 units of the product is:

\[ \text{Marginal Revenue} = 21 \]

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