Learn how to find the derivative of x^2 y. The derivative is d/dx[x^2 y].
Below is the graph of f(x) = x^2 y 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.
Recognizing that x^2 y involves a product of x^2 and y, we determine that Power Rule applies to the x^2 term, as y is independent of x.
💡 Why this works: The Power Rule is applied to x^2, while y is treated as a constant, meaning it doesn't change as x changes.
Using the Power Rule, we differentiate the x^2 term. The derivative of x^2 is 2x, and y remains unchanged.
💡 Why this works: By differentiating x^2 as per the Power Rule, we get 2x, and since y is constant, it is simply multiplied by the result.
The derivative of x^2 y simplifies to 2x y. This is the correct form because the derivative of x^2 is 2x, and y is a constant factor.
💡 Why this works: The final derivative is 2x y, which shows how the function x^2 y changes with respect to x, with y acting as a constant multiplier.
[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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