Questions in derivatives I want to check my answer

  • Thread starter Thread starter r-soy
  • Start date Start date
  • Tags Tags
    Derivatives
Click For Summary
SUMMARY

The discussion focuses on common mistakes in solving derivative problems, specifically addressing errors in algebraic manipulation. The first mistake involves incorrectly expanding the expression (x + 0.5)², which does not equal x² + 0.25. The second mistake pertains to the multiplication of (x² - 1)(x² + x + 1), where the participant failed to apply the correct multiplication rules. The correct approach emphasizes the importance of distinguishing between factors and terms in algebraic expressions.

PREREQUISITES
  • Understanding of basic algebraic operations
  • Familiarity with derivative concepts
  • Knowledge of polynomial multiplication
  • Ability to identify factors versus terms in expressions
NEXT STEPS
  • Review polynomial expansion techniques
  • Study the rules of algebraic manipulation in calculus
  • Practice identifying factors in algebraic expressions
  • Learn about common errors in derivative calculations
USEFUL FOR

Students studying calculus, mathematics educators, and anyone looking to improve their skills in algebraic manipulation related to derivatives.

r-soy
Messages
170
Reaction score
1
Last edited by a moderator:
Physics news on Phys.org
Post the question and your answer, then?
 
1 and 2 are incorrect. 3 is correct.

There are two mistakes in #1.
(x + .5)2 \neq x2 + .25

The cancelling you did is incorrect. The only time you can cancel is when the same factor appears in the numerator and denominator. You canceled terms (things that are added together) rather than factors (things that are multiplied together).

In 2, there is an error when you multiplied (x2 - 1)(x2 + x + 1).
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
9
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
22
Views
3K