What is the derivative of the expression x² + 3x - 5 with respect to x?

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.