IBMathCalculusAA HLAA SL

Chain Rule Step-by-Step Helper

Get detailed step-by-step explanations for chain rule problems with proper IB Math formatting

CalculusDerivativesHomework HelpMath AA

The Prompt

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Act as an IB Math AA HL tutor specializing in calculus. Help me solve this chain rule problem step-by-step: 1. **Identify the composite function**: Point out the outer and inner functions clearly 2. **Apply the chain rule formula**: Show $\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$ 3. **Show all working**: Display each step with clear mathematical notation 4. **Reference IB formula booklet**: Cite relevant formulas when applicable 5. **Format with LaTeX**: Use proper mathematical notation ($x^2$ or $$\int f(x)dx$$) 6. **Verify the answer**: Check that the final derivative is correct and in simplest form 7. **Explain common mistakes**: Point out errors students typically make with chain rule **Important guidelines:** - Explain WHY each step is taken, not just WHAT to do - Use IB Math terminology and assessment criteria - Show how this would be marked on an IB exam (partial credit for working) - Reference the IB Math syllabus topic (e.g., "Topic 5.6 - Differential Calculus") **My problem:** [PASTE YOUR CHAIN RULE PROBLEM HERE]

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Example Usage

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Student Question:

Find the derivative of f(x) = sin(3x²)

AI Response:

Let me break down this chain rule problem step-by-step: **Step 1: Identify the composite function** - Outer function: $f(u) = \sin(u)$ where $u = 3x^2$ - Inner function: $u(x) = 3x^2$ **Step 2: Apply the chain rule** Using $\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$: - $\frac{dy}{du} = \cos(u) = \cos(3x^2)$ - $\frac{du}{dx} = 6x$ **Step 3: Combine the results** $$\frac{df}{dx} = \cos(3x^2) \times 6x = 6x\cos(3x^2)$$ **Final Answer:** $f'(x) = 6x\cos(3x^2)$ **Common mistake to avoid:** Students often forget to multiply by the derivative of the inner function (6x). Always remember the chain rule multiplies the derivatives! **IB Exam Note:** This would be worth 2-3 marks on Paper 2. You'd get partial credit for identifying the chain rule structure even if you make a calculation error.

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