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Calculus · Studypool

Checklist for Derivative Rules Discussion

Post ID: 1311519

Overview

This week, you were introduced to different derivative rules. Determine which rules should be used when taking the derivative of one of the functions below.

  1. For your main post, choose ONE of the functions from the list:
    1. A. f of x equals the square root of open bracket x squared plus two x minus one close bracket, divided by open bracket x + three close bracket
    2. B. f of x equals the product of open bracket three x to the seventh power, plus five close bracket raised to the fifth power, and open bracket five minus x close bracket) to the seventh power
    3. C. f of x equals open bracket four x squared minus three close bracket, divided by open bracket x plus three close bracket all raised to the fifth
    4. D. f of x equals three x to the fifth power, times the square root of open bracket six x squared plus one close bracket
    5. E. f of x equals open bracket two x plus 5 close bracket, over the square root of open bracket three x squared plus eight close bracket
  2. After your selection, develop a process document (flowchart, checklist, etc.) that explains your thought process in deciding which particular approach or method to use to determine which derivative rules apply.

It is not necessary to give a final answer of what the derivative of the function is. The purpose is to walk us through how you would take the derivative of the function by identifying the necessary rules that apply in the process.

Type your solution in the discussion text box or post it as an attachment. Be sure to identify which function you chose in the post. Remember that your process should be clear enough for another person to follow.

After you have made your initial post, evaluate at least two classmates’ process documents and determine your ability to follow the steps they provided. Provide feedback on clarity, direction, and interpretation of the rules from this week.

FIRST POST 

Greetings everyone,

For this discussion, I have chosen to analyze option B. I apologize if this is hard to follow. I tried to demonstrate each step that I took to find the answer but I struggle significantly at showing my processes for answering problems. This was compounded by not having a good tool at my disposal for writing each step to show how it would work. So, hopefully it doesn't come across as too abstract.

1. Identify the problem - this function is the product of two equations which allows the use of the product rule. f(x)=(3x^7+5)^5(5?x^7)

2. Apply the product rule to find f'.

ddx((3x^7+5)^5)

3. Apply the chain rule.

ddu(u^5)ddx(3x^7+5)

4. Apply the power rule.

5u^4

5. Apply the sum/difference rule.

ddx(3x^7)+ddx(5)

6. Apply the power rule and simplify.

21x^6

7. Substitute 3x^7+5 for u.

(5(3x^7+5)^4)(21x^6)

8. Simplify

105x^6(3x^7+5)^4

9. Apply the chain rule to begin finding g' from ((5-x)^7)

ddu(u^7)ddx(5?7)

10. Apply the power rule and simplify.

7u^6

11. Apply the sum/difference rule to (5-x) and simplify.

7u^6(?1)

12. Substitute for u and simplify.

?7(5?x)^6

13. Recombine the parts of the equation to get the answer.

ddxf=105x^6(3x^7+5)^4(5?x)^7?7(5?x)^6(3x^7+5)^5

SECOND POST

I choose option B.

First, I would recognize this as a rational function:

f(x) = (3x7+5)5(5?x)7

Then I would apply the product rule to get the derivative of the first part times the second part plus the derivative of the second part times the first part:

f'(x) = ddx(3x7+5)5·(5?x)7+ ddx(5?x)7·(3x7+5)5

I would then take the derivatives using the chain rule:

f'(x) = 5(3x7+5)4(21x6)(5?x)7+7(5?x)6(?1)(3x7+5)5

I would then simplify this into:

f'(x) = 105x6(3x7+5)4(5?x)7?7(5?x)6(3x7+5)5

John