Learn how to find the derivative of x^2 - 3x. The derivative is d/dx[x^2 - 3x].
Below is the graph of f(x) = x^2 - 3x and its derivative f'(x). Notice how the original function and derivative relate to each other.
Original Function:
Derivative:
This derivative represents the rate of change of the original function. The calculation follows standard differentiation rules as shown in the step-by-step solution below.
We start by recognizing the terms in the expression x^2 - 3x. The first term, x^2, is a polynomial, and the second term, -3x, is a linear term. The Power Rule is applicable to both of these terms because they follow the form of a variable raised to a power.
💡 Why this works: The Power Rule is used here because both terms involve powers of x: x^2 and x^1. This rule allows us to differentiate each term independently.
Using the Power Rule, we differentiate each term. For x^2, the derivative is 2x (we multiply the exponent by the coefficient and subtract 1 from the exponent). For -3x, the derivative is -3 (since the exponent of x is 1, and applying the rule gives us the coefficient).
💡 Why this works: Applying the Power Rule to x^2 gives 2x, and applying it to -3x results in -3. This step-by-step application yields the derivative d/dx[x^2 - 3x] = 2x - 3.
The derivative is already in its simplest form: 2x - 3. There are no further simplifications needed.
💡 Why this works: The result of d/dx[x^2 - 3x] = 2x - 3 is the correct final derivative. It reflects the rate of change of the function at any point along its curve.
[Teaching explanation - to be filled]
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❌ Common Mistake:
Not simplifying the final answer
✅ Correct Approach:
Always simplify your derivative to its most reduced form
Double-check your work by comparing your steps with our solution. Use our calculator to verify each step of the differentiation process.
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