Derivative of 4/sqrtx Using the Limit Process

  • Thread starter Chunkysalsa
  • Start date
  • Tags
    Limit
In summary, the conversation is about finding the derivative of a function using the limit process. The person asking the question has tried various methods but is struggling to simplify the answer. They eventually figure it out on their own after taking a break.
  • #1
Chunkysalsa
311
0

Homework Statement


Find the derivative of 4/sqrtx using the limit process

Homework Equations





The Attempt at a Solution



I know the method and I even know the answer using other (easier) means but I just cannot simplify it. I've tried almost everything i can think of. I feel like this is an easy answer but I'm just not seeing it.

I tried rationalizing the numerator and that helps me with taking the actual limit but I'm having problems simplifying to the correct answer.
 
Physics news on Phys.org
  • #2
Show us what you tried and we'll help you with this problem.
 
  • #3
Never mind, like I said easy problem just couldn't see it.

Ate lunch and came back to it and it all made sense. Thanks anyway
 

1. What is the formula for finding the derivative of 4/sqrtx using the limit process?

The formula for finding the derivative of a function using the limit process is:
f'(x) = lim(h->0) (f(x+h) - f(x)) / h

2. How do you simplify the expression 4/sqrtx before taking the limit?

In order to simplify the expression 4/sqrtx, you can rewrite it as 4x^(-1/2). Then, you can apply the power rule for derivatives to get -2x^(-3/2).

3. Can the limit process be used to find the derivative of any function?

Yes, the limit process can be used to find the derivative of any function, as long as the function is continuous and differentiable at the point being evaluated.

4. Why is the limit process used to find derivatives?

The limit process is used to find derivatives because it is a general method that can be applied to any function. It involves taking the limit of a difference quotient, which represents the slope of a tangent line at a specific point on a curve.

5. How does the limit process for finding derivatives relate to the concept of instantaneous rate of change?

The limit process for finding derivatives is directly related to the concept of instantaneous rate of change. The derivative of a function at a specific point represents the instantaneous rate of change of the function at that point. By taking the limit of a difference quotient, we are essentially finding the slope of the tangent line at that point, which is the instantaneous rate of change.

Similar threads

Question re: Limits of Integration in Cylindrical Shell Equation
    • Calculus and Beyond Homework Help
Replies
24
Views
2K
How can I use integration by tables to solve sin^-1(sqrtx)?
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Multivariable calculus problem involving partial derivatives along a surface
    • Calculus and Beyond Homework Help
Replies
9
Views
714
How can finding limits by conjugates be used to solve for rational expressions?
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Relating limits to derivatives, as x approaches non zero number?
    • Calculus and Beyond Homework Help
Replies
5
Views
2K
Limit question to be done without using derivatives
    • Precalculus Mathematics Homework Help
Replies
25
Views
765
How can you determine the following limit
    • Calculus and Beyond Homework Help
Replies
20
Views
2K
Solving Limits: Finding a, b, c, and d for ∞-∞ Form
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Limit of a multivariable function
    • Calculus and Beyond Homework Help
Replies
6
Views
2K
Finding limits with a radical in denominator
    • Calculus and Beyond Homework Help
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top