How Do I Solve 1st and 2nd Derivative Homework Problems?

  • Thread starter Thread starter LiHJ
  • Start date Start date
  • Tags Tags
    Derivative
Click For Summary
SUMMARY

The discussion focuses on solving first and second derivative homework problems, specifically addressing differentiation techniques. A participant suggests using trigonometric identities, such as replacing sec(x) with 1/cos(x) and transforming the logarithmic argument to (1+sinx)/cos(x) before applying differentiation. This method streamlines the differentiation process and provides an alternative approach to solving the problems presented in the textbook. The conversation emphasizes the importance of understanding differentiation fundamentals for effective problem-solving.

PREREQUISITES
  • Understanding of basic calculus concepts, particularly differentiation.
  • Familiarity with trigonometric identities, specifically secant and cosine functions.
  • Knowledge of logarithmic functions and their properties.
  • Ability to manipulate algebraic expressions for simplification.
NEXT STEPS
  • Study advanced differentiation techniques, including implicit differentiation.
  • Learn about the application of trigonometric identities in calculus.
  • Explore logarithmic differentiation for complex functions.
  • Practice solving derivative problems using various methods and tools.
USEFUL FOR

Students studying calculus, mathematics educators, and anyone seeking to improve their skills in solving derivative problems effectively.

LiHJ
Messages
43
Reaction score
2

Homework Statement



Dear Mentors PF Helpers,

Here's my question:

image.jpg


I see it from my textbook with it solutions copied down below. Wonder is there another way to do it.
Thank you for your time.

Homework Equations



image.jpg
[/B]

The Attempt at a Solution


image.jpg
 
Physics news on Phys.org
I do not see that you did any differentiation.
 
Sorry forgot to copied these as well

image.jpg
 
I do not see any other way than doing the differentiation. You may replace sec(x) by 1/cos(x), and replace the argument of the logarithm by (1+sinx)/cos(x) before differentiating.
 
Thank you
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
9
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 11 ·
Replies
11
Views
2K
Replies
6
Views
2K