MathematicsChapter 2: Limit, Continuity and Derivative
Power, Constant, and Sum Rules
d(x^n)/dx=n x^(n-1); differentiate sums term by term and constants to zero.
Learning objectives
- State the rule for power, constant, and sum rules.
- Solve a power, constant, and sum rules problem step by step.
- Check the result, restrictions, notation, and units.
Definition
d(x^n)/dx=n x^(n-1); differentiate sums term by term and constants to zero.
Mathematical form
dx=n x(n-1)
dx=12x2-2.
Where / symbols
- Power, constant, and sum rules
- d(x^n)/dx=n x^(n-1); differentiate sums term by term and constants to zero.
CONCEPT AND RULE
d(x^n)/dx=n x^(n-1); differentiate sums term by term and constants to zero.
METHOD
For power, constant, and sum rules, 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(4x3-2x+7)/dx=12x2-2.
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 power, constant, and sum rules
- 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.
Worked example
- Worked example:
- d(4x3-2x+7)/dx=12x2-2.
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Power, constant, and sum rules
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Power, Constant, and Sum Rules
Sticky Notes · Formula and Worked Revision
Core Idea
- d(x^n)/dx=n x^(n-1); differentiate sums term by term and constants to zero.
Rule / Formula
- d(x^n)/dx=n x^(n-1); differentiate sums term by term and constants to zero.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- d(4x3-2x+7)/dx=12x2-2.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- d(x^n)/dx=n x^(n-1); differentiate sums term by term and constants to zero.
- Worked pattern: d(4x3-2x+7)/dx=12x2-2.
- Final check: domain, sign, notation, units, and reasonableness.
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