Derivative of x² + 3x - 2

Published on October 13, 2024

Calculus

Learn how to find the derivative of the function f(x) = x² + 3x - 2 using the power rule, constant multiple rule, and sum/difference rule. The derivative is f'(x) = 2x + 3.

Question

Find the derivative of f(x) = x² + 3x - 2

Answer

Let’s find the derivative of f(x) = x² + 3x - 2 step-by-step.

1. Power Rule:

The power rule states that the derivative of x^n is nx^(n-1).

2. Constant Multiple Rule:

The constant multiple rule states that the derivative of a constant times a function is equal to the constant times the derivative of the function.

3. Sum/Difference Rule:

The sum/difference rule states that the derivative of a sum or difference of terms is the sum or difference of the derivatives of those terms.

Applying the Rules:

Term 1 (x²):
- Using the power rule, the derivative of x² is 2x^(2-1) = 2x.
Term 2 (3x):
- Using the constant multiple rule, we can factor out the constant 3: 3 * (d/dx)(x).
- The derivative of x is 1, so the derivative of 3x is 3 * 1 = 3.
Term 3 (-2):
- The derivative of a constant is always 0.