Learn how to find the derivative of xy. The derivative is d/dx[xy].
Below is the graph of f(x) = xy 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.
xy involves the product of x and y. The Power Rule applies because x is raised to the first power and is part of a product with another variable, y.
💡 Why this works: In this case, the function xy fits the conditions for applying the Power Rule because x is treated as a variable raised to the first power. The function's structure is simple enough for Power Rule to be effective, allowing differentiation of each part of the product individually.
To differentiate xy with respect to x, apply the Power Rule to x and treat y as a constant.
💡 Why this works: Using the Power Rule, differentiate x, which gives 1, while y remains unchanged. This results in d/dx[xy] = y. The derivative of xy is the constant y because the derivative of x is 1, and y does not depend on x.
The simplified form of the derivative is d/dx[xy] = y, as no further simplification is necessary.
💡 Why this works: Since y is treated as a constant, the derivative of xy with respect to x simplifies directly to y. This is the correct final form because the derivative of a constant with respect to x is 0, and only the term involving x contributes to the derivative.
[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.
Calculate any derivative instantly with step-by-step solutions. Perfect for students, teachers, and anyone learning calculus.