Learn how to find the derivative of x^2. The derivative is 2x.
Below is the graph of f(x) = x^2 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.
The function x^2 is a power function, where the exponent is 2. This structure fits perfectly with the Power Rule, which is used to differentiate functions of the form x^n.
💡 Why this works: The Power Rule applies because x^2 is a polynomial with a constant exponent, making it straightforward to differentiate.
To differentiate x^2, we apply the Power Rule: bring down the exponent (2) and subtract 1 from the exponent. This gives us 2x^(2-1), or simply 2x.
💡 Why this works: By following the Power Rule, we obtain the derivative 2x, which represents the instantaneous rate of change of x^2.
After applying the Power Rule, the derivative simplifies to 2x. This is the final result.
💡 Why this works: 2x is the correct form of the derivative, as it reflects the slope of the tangent line to the curve of x^2 at any point.
[Teaching explanation - to be filled]
[Application to this function - to be filled]
❌ 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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