Solving the Derivative of f(a): A Frustrating Homework Problem

In summary, the conversation is about finding the derivative of a function and the use of the quotient rule. The original poster was having trouble getting the correct answer and another user provided a simplified solution. However, there was a mistake in the variables used and the correct solution is still being discussed.
  • #1
fghtffyrdmns
145
0

Homework Statement


For some reason, I cannot seem to get the derivative for this.


Homework Equations



[tex] f(a) =\frac {(2500+0.2t)(1+t)}{\sqrt {0.5t+2}}[/tex]

The Attempt at a Solution



[tex] f(a) =\frac {(2500+0.2t)(1+t)}{\sqrt {0.5t+2}}[/tex]

c1fb89063c9c2285cffa29f34ca44490.png


[tex]\frac {(2500+0.2t)}{\sqrt {0.5t+2}} (1+t)[/tex]

From here I would just use the quotient rule but I keep getting the wrong answer and I have no idea why.
 
Physics news on Phys.org
  • #2
I'll simplify this for you. See if you can solve the question from here:

First, FOIL the numerator. Next, solve all of our components separately, so:

h'(x) = [tex]\frac{d}{dx}[/tex] (0.5t + 2)1/2

= [tex]\frac{1}{2}[/tex](0.5t +2)-1/2 * 0.5 <By Chain Rule>

= [tex]\frac{1}{4}[/tex] [tex]\frac{1}{\sqrt{(0.5t+2)}}[/tex] <By x^-1 = 1/x>

g'(x) = 0.4t + 2500.2 <By power rule x^2 = 2x when the derivitive is taken>

h(x)2 = 0.5t + 2 <x^1/2^2 = x^1>

next, plug in all of that data to the quotient rule, simplify, and see what you get!
 
  • #3
ahhh, thank you!

at first, I thought I was supposed to treat it separately. Now, I just expanded the numerator and took the derivatives of both sides.

Thank you, sir :).
 
  • #4
Both of you should get your variables straight.
fghtffyrdmns said:
[tex] f(a) =\frac {(2500+0.2t)(1+t)}{\sqrt {0.5t+2}}[/tex]
That would be f(t), not f(a).
RPierre said:
h'(x) = [tex]\frac{d}{dx}[/tex](0.5t + 2)1/2
And that would be [tex]h'(t) = \frac{d}{dt}(0.5t + 2)^{1/2}[/tex]
 
Last edited:
  • #5
I'm not familiar with LaTex and assumed he wasn't using leibniz notation by the prime notation used and the level of calculus, so I simply whipped up a solution with simple principles. I'm sure the original poster got the point as the question was able to be resolved.

Thanks for pointing that out though, I'll be more precise with my answers in the future, I'm also new to these forums.
 
  • #6
ah yes, it's my fault. I wrote the wrong variables in accidentally.I got this as my answer

[tex] \frac {(0.5t+2)^{1/2}(0.4t+2500.2)-(2500+2500.2t+0.2t^{2})}{(2t+8)^{3/2}}[/tex]
 
Last edited:
  • #7
Hmm. This is not the right derivative. Where did I go wrong?
 

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is the slope of the tangent line to the function at that point.

Why is solving the derivative of f(a) a frustrating homework problem?

Solving the derivative of f(a) can be frustrating because it requires a deep understanding of calculus concepts and techniques. It involves complex calculations and can be time-consuming, making it a challenging homework problem for many students.

What is the purpose of solving the derivative of f(a)?

The purpose of solving the derivative of f(a) is to find the instantaneous rate of change of a function at a specific point. This is useful in many real-world applications, such as calculating velocity, acceleration, and optimization problems.

What are some common techniques for solving the derivative of f(a)?

Some common techniques for solving the derivative of f(a) include the power rule, product rule, quotient rule, chain rule, and implicit differentiation. These techniques involve differentiating with respect to a variable and using algebraic manipulations to simplify the expression.

How can I improve my skills in solving the derivative of f(a)?

To improve your skills in solving the derivative of f(a), practice is key. Work through a variety of problems using different techniques and seek help from a teacher or tutor if needed. Also, make sure to review and understand the underlying concepts of calculus, as they are crucial for mastering derivatives.

Similar threads

  • Calculus and Beyond Homework Help
Replies
9
Views
905
  • Calculus and Beyond Homework Help
Replies
4
Views
502
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
Replies
9
Views
646
  • Calculus and Beyond Homework Help
Replies
6
Views
489
  • Calculus and Beyond Homework Help
Replies
7
Views
809
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
Replies
7
Views
439
  • Calculus and Beyond Homework Help
Replies
16
Views
1K
  • Calculus and Beyond Homework Help
Replies
23
Views
834
Back
Top