The simplified derivative of the function (50t)/(6+t)^3 can be accurately derived using the quotient rule. The correct answer is (-100(t - 3))/(6 + t)^4, as stated in the textbook. The common mistake involves overcomplicating the numerator after applying the quotient rule. Instead, factoring out common elements simplifies the expression effectively, leading to the correct result.
PREREQUISITESStudents studying calculus, particularly those struggling with derivative simplification techniques, and educators looking for examples to illustrate common mistakes in applying the quotient rule.
To get the book's answer, don't multiply things out in the numerator after you use the quotient rule. In the numerator, both terms have a factor of 50 and a factor of (6 + t)2. Bring out these factors, and what you have left is easy to simplify, and results in the book's answer.939 said:Homework Statement
I keep getting it wrong. Using the quotient rule.
Homework Equations
Derivative of (50t)/(6+t)^3
The Attempt at a Solution
My answer: -100t^3 - 900t^2 + 10800/((6+t)^3)^2)
The book: (-100 (t - 3))/(6 + t)^4
What happened?
EDIT: Nevermind, I realize they're basically the same. I'll leave this here incase someone needs help in the future.