- Difficulty
- Introductory
- Suggested time
- 3 min
- Marks
- 2
Differentiation rules practice question 2
A student differentiates as shown below. Which line contains the first error?
Check each line against what it claims to do: line 1 applies a differentiation rule, and lines 2 and 3 tidy up the line before. Can you write that rule from memory?
Write the quotient rule out in full before comparing: . Check the sign between the two terms.
Theory UBC Math 100 §4.1CLP-1 §2.6Key results
Worked solution
Strategy
Compare each line against the rule it claims to apply. Lines 2 and 3 are correct algebra on what came before them; the error is in the rule itself.
Working
Name the parts.
The rule subtracts. Line 1 added, and everything after it inherits the mistake.
Answer
The answer is the error is in line 1; the correct derivative is 5(1 − x²) over (x² + 1)².
Check
f(1) = 2.5 is the largest value of f, so f′(1) must be 0, but line 3 gives 5 there.
Where this goes wrong
Hunting for an arithmetic slip in lines 2 and 3, which are both correct, instead of checking the rule in line 1. When a derivative looks wrong, check the rule before the algebra.
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