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Product Rule
For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.
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Product Rule
What is it?
For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.
In simple words
- For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.
- Worked pattern: d[x2 sin x]/dx=2x sin x+x2 cos x.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Product rule: For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.
What you should learn
- State the rule for product rule.
- Solve a product rule problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.
CONCEPT AND RULE
For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.
METHOD
For product rule, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
d[x2 sin x]/dx=2x sin x+x2 cos x.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve product rule
How it works
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Remember
- Product rule
- rule
- worked example
- worked example
How the ideas connect
Worked example: d[x2 sin x]/dx=2x sin x+x2 cos x.
Deeper understanding
Go beyond memorising Product Rule. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: d[x2 sin x]/dx=2x sin x+x2 cos x.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Product rule
- rule
- worked example
- Product rule: For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.
- CONCEPT AND RULE: For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.
- METHOD: For product rule, identify the given information and required result. Select the matching definition
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Product Rule: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Product rule
- rule
- worked example
- Product rule: For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.
Important formulas
- Product rule
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Product rule
rule
worked example
Product rule: For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.
For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.
- Definition
- For y=uv, y'=u'v+uv'; differentiating each factor separately and multiplying is wrong.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Product Rule.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Product Rule and say why it fits.
Mistake
Q4. State one common mistake students make about Product Rule.
Exam note
Q5. Write a short exam note on Product Rule: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.