Learn how to find the derivative of x^3 sin(2x). The derivative is d/dx[x^3 sin(2x)].
Below is the graph of f(x) = x^3 sin(2x) 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.
Analyze the structure of x^3 sin(2x) to determine which differentiation rules apply.
💡 Why this works: The function x^3 sin(2x) requires Trigonometric Rule, Power Rule based on its mathematical structure.
Apply Trigonometric Rule, Power Rule to find the derivative components.
💡 Why this works: Following the rules systematically leads to d/dx[x^3 sin(2x)].
Combine and simplify to get the final derivative d/dx[x^3 sin(2x)].
💡 Why this works: Simplification ensures the derivative is in its most useful form.
[Teaching explanation - to be filled]
[Application to this function - to be filled]
❌ Common Mistake:
Confusing the derivatives of sin(x) and cos(x)
✅ Correct Approach:
Remember: d/dx[sin(x)] = cos(x), d/dx[cos(x)] = -sin(x)
❌ 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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