Algebra Practice Test 2026 – The Complete Guide to Mastering Your Exam Success!

To find the derivative of the expression \( x^2 + 3x - 5 \) with respect to \( x \), we apply the basic rules of differentiation.

The power rule states that the derivative of \( x^n \) (where \( n \) is a constant) is \( n \cdot x^{n-1} \).

1. For the term \( x^2 \), the derivative is \( 2 \cdot x^{2-1} = 2x \).

2. For the term \( 3x \), the derivative is simply \( 3 \), since the derivative of \( x \) is \( 1 \).

3. The derivative of a constant, like \( -5 \), is \( 0 \).

Putting these results together, the overall derivative is:

\[

2x + 3 + 0 = 2x + 3

\]

Thus, the derivative of the given expression \( x^2 + 3x - 5 \) with respect to \( x \) is indeed \( 2x + 3 \). This confirms that the correct answer is the one which reflects these calculations accurately.