- #1
mathmann
- 37
- 0
Just wondering how you take the second derivative when using the quotient rule. After using the quotient rule to get my first derivative, I tried again and the numerator ended up as 0.
Taking the Second Derivative w/ the Quotient Rule: What if Numerator = 0?
- Thread starter mathmann
- Start date
In summary, the conversation discusses using the quotient rule to find the second derivative and determining whether an object is speeding up at a certain time. The conversation also clarifies the process for finding the acceleration at a specific time and emphasizes the importance of differentiating the velocity function before substituting in a fixed time.
- #2
yenchin
- 544
- 3
Can you show us your exact working?
- #3
mathmann
- 37
- 0
s(t) = t^2 - 2/t + 1, is the object speeing up at 4s?
v(t) = 1.04, a(t) the numerator ended up as a 0. Perhaps I made a calculating error but I went over it a couple times.
v(t) = 1.04, a(t) the numerator ended up as a 0. Perhaps I made a calculating error but I went over it a couple times.
- #4
yenchin
- 544
- 3
You mean s(t) = (t^2 - 2)/(t + 1) right?
Then v(t) = (t^2 + 2t + 2)/(t+1)^2
and a(t) = - 2/ (t+1)^3
Then v(t) = (t^2 + 2t + 2)/(t+1)^2
and a(t) = - 2/ (t+1)^3
- #5
yenchin
- 544
- 3
When you evaluate v(t) at some fixed t you get the velocity at that point in time. You are not supposed to differentiate that particular velocity to get the acceleration at that time. You need to work out a(t) first by differentiating the function v(t) before substituting in your fixed t.
- #6
mathmann
- 37
- 0
I understand now.. thanks for the help.
- #7
yenchin
- 544
- 3
No problem 
Related to Taking the Second Derivative w/ the Quotient Rule: What if Numerator = 0?
What is the quotient rule for taking the second derivative?
The quotient rule for taking the second derivative is a formula used to find the derivative of a function that is the quotient of two other functions. It states that the second derivative of the quotient function is equal to the difference of the second derivative of the numerator function and the product of the first derivative of the numerator function and the first derivative of the denominator function, all divided by the square of the denominator function.
When do I use the quotient rule for taking the second derivative?
The quotient rule for taking the second derivative is used when you have a function that is the quotient of two other functions, and you want to find the second derivative of that function. This rule is particularly useful when the two functions involved are too complicated to differentiate using the basic rules of differentiation.
What do I do if the numerator is equal to 0 when using the quotient rule for taking the second derivative?
If the numerator of the quotient function is equal to 0, you can simplify the quotient function before applying the quotient rule for taking the second derivative. This can be done by factoring out the common factor of the numerator and then simplifying the resulting function. Once simplified, you can then use the quotient rule to find the second derivative.
Can I use the quotient rule for taking the second derivative if the denominator is equal to 0?
No, the quotient rule for taking the second derivative cannot be applied if the denominator of the quotient function is equal to 0. This is because division by 0 is undefined in mathematics. If the denominator is equal to 0, you will need to use a different method, such as the product rule or chain rule, to find the second derivative of the function.
What are the common mistakes to avoid when using the quotient rule for taking the second derivative?
One common mistake is forgetting to simplify the function before applying the quotient rule when the numerator is equal to 0. Another mistake is mixing up the order of the terms in the quotient rule formula. It is important to remember that the second derivative of the quotient function is equal to the difference of the second derivative of the numerator function and the product of the first derivatives of the numerator and denominator functions. Finally, be careful when dealing with functions that have multiple terms in the numerator or denominator, as it can be easy to make a mistake when differentiating each term.
Similar threads
-
Mechanics
-
Calculus and Beyond Homework Help
-
STEM Educators and Teaching
-
General Math
-
Calculus
-
Calculus and Beyond Homework Help
-
Science and Math Textbooks