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

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

• A. \(3x + 5\)
• B. \(6x + 5\)
• C. \(5x + 3\)
• D. \(6x + 3\)

Answer: (B)

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

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