Finding the nth Derivative of a Rational Function

  • Thread starter powp
  • Start date
In summary, the conversation is about finding the function f^(n)(x) for 1/(5x-1) and the top portion of the function. The hint given is to leave the coefficients factored and the final answer involves a factorial and something else. The person eventually figures out the answer to be -1^2(n!)5^n*(5x-1)^(-1-n).
  • #1
powp
91
0
Hello

I have this problem that I cannot get part of. I need function f^(n)(x) for 1/(5x-1). I have been working it out and I know the denominator is going to be (5x-1) ^ (n+1) but can not figure out the top.

So my question is how do I create a statement that evalutes the following

when x = 1 it equal -5
when x = 2 it equals -5 * -10 == 50
when x = 3 it equals -5 * -10 * -15 == -750

any hints would be great

Thanks

Peter
 
Physics news on Phys.org
  • #2
Here's a hint

powp said:
Hello
I have this problem that I cannot get part of. I need function f^(n)(x) for 1/(5x-1). I have been working it out and I know the denominator is going to be (5x-1) ^ (n+1) but can not figure out the top.

Hint: as you differentiate, leave the coefficients factored. The answer your looking for involves a factorial and something else.
 
  • #3
Thanks. This is driving me crazy. I have been thinking is has to do with factorials all this time but not sure in what way.
 
  • #4
Please help

Can anybody please help me I am stuck. Please please please
 
  • #5
Think I finally got it my answer -1^2(n!)5^n*(5x-1)^(-1-n)

Thanks for your help
 

FAQ: Finding the nth Derivative of a Rational Function

What is the importance of finding an equation?

Finding an equation is essential in scientific research and experimentation. It allows us to mathematically describe and understand the relationship between different variables and phenomena. Equations also help us make predictions and test hypotheses, making them crucial in the scientific method.

How do I find an equation for my data?

There are different methods for finding an equation, depending on the type of data and the variables involved. In general, you will need to analyze your data, look for patterns and trends, and use mathematical tools such as regression analysis or curve fitting to find the best-fit equation. Consulting with a statistician or using software programs can also be helpful.

Can I use any equation for my data?

No, not all equations are suitable for every type of data. The equation you use should be based on the variables and the relationship between them. It should also accurately represent your data and have a high level of statistical significance.

What if I can't find an equation for my data?

Some data sets may not have an exact equation that fits them perfectly. In such cases, it is still possible to use approximations or simplified equations to describe the relationship between the variables. It is also important to consider the limitations of your data and the potential for error in your measurements.

Can I manipulate an equation to fit my data?

No, manipulating an equation to fit your data is not a valid scientific approach. The equation should be derived from the data, not the other way around. Manipulating an equation can lead to incorrect conclusions and should be avoided in scientific research.

Similar threads

Find the derivative of the given function
Replies
4
Views
1K
How Do You Simplify and Analyze Taylor Polynomials for Higher Degree Functions?
Replies
5
Views
1K
Finding the Fourier Series of a step function
Replies
5
Views
2K
Proving convergence of rational sequence
Replies
2
Views
862
Odd/even function and critical points
Replies
4
Views
2K
Derivative of Secant: Find dy/dx
Replies
2
Views
1K
Understanding the Derivative of a Polynomial with Exponent 10
Replies
13
Views
2K
Derivative of Inverse Function
Replies
14
Views
1K
Rational epsilon-delta limit proof questions
Replies
9
Views
3K
Finding the nth derivative of a function
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top