What is the derivative of \(f(x) = 3x^2 + 5x\)?

To find the derivative of the function (f(x) = 3x^2 + 5x), we can apply the power rule. The power rule states that the derivative of (x^n) is (n \cdot x^{n-1}), where (n) is a constant.

For the term (3x^2), we see that (n) is 2. Therefore, applying the power rule gives us:

1. Multiply the coefficient (3) by the exponent (2) to get (3 \cdot 2 = 6).

2. Then decrease the exponent by 1, changing (x^2) to (x^1).

Thus, the derivative of (3x^2) is (6x).

Next, we differentiate the second term (5x). Since (x) is (x^1), we apply the power rule again:

1. Multiply the coefficient (5) by the exponent (1) to obtain (5 \cdot 1 = 5).

2. Decrease the exponent, which leads us to simply (5x^0).

Because (x^0