Solve f'(x): f'(x) Solution

  • Thread starter alba_ei
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In summary, the conversation is about finding the derivative of the given function and discussing different methods for differentiation. The participants suggest using various rules of differentiation and offer resources for further assistance. The conversation ends with the suggestion to use the quotient rule when finding the derivative of R(x).
  • #1
alba_ei
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Who can slove this one:

f(x) = [ln(x) {{1-e^(3x)}^3}] / [{1+e^(3x)}^3x]

f '(x) = ¿¿¿¿??
 
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  • #2
Again, please show your work for this homework question. What methods of differentiation do you know of?
 
  • #3
alba_ei,

This is not difficult but a little bit long to write.
What is your objective?
Is it for some homework, or do you have a practical application?

For an homework, the result would not be helpful for you, only the method matters.
There are only known functions in this expression: products, divisions, logarithm, exponential.
Reading a table of derivatives rules and a bit of patience is enough.
On wiki you can find the basis about derivatives and the http://en.wikipedia.org/wiki/Derivative" [Broken].

For a practical application, more details would be needed to decide how to proceed for the best result.
If this derivative is the only one in the project, then using a software like Mathematica could avoid any typing error.
If you only need numerical results, then "Numerical Recipes" explains what to care for.

Michel
 
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  • #4
alba_ei,

As lalbatros suggests, this may be long and messy. But consider breaking this down into managable parts. For example, let your function be

f(x) = ln(x)*R(x)

where R(x) = P(x)/Q(x)

Then, apply the various rules of differentiation (product, quotient, etc) to perform the derivative. Start simply, and break each component down.

For example, start with

f'(x) = [ln(x)]' * R(x) + ln(x) *R'(x)

In the end, you should be able to find an expression for f'(x) in the form

f'(x) = R(x) * W(x)

where W(x) = 1/x + ln(x) * s(x) (you find s(x))

Give it a try, and come back if you still get stuck.
 
  • #5
well, I saw that derivate on some past exam so the last night I remmember it and post it, just for curiosity because I can't slove it.

f(x) = ln(x)*R(x)

where R(x) = P(x)/Q(x)

I get stuck when I try to get the derivate of R(x).
 
  • #6
alba_ei said:
I get stuck when I try to get the derivate of R(x).

Use the quotient rule: [tex]R'(x)=\frac{Q(x)P'(x)-P(x)Q'(x)}{Q(x)^2}[/tex]
 

What is the definition of f'(x)?

The derivative of a function f(x) is denoted by f'(x) and represents the rate of change of the function at a specific point x.

How do you solve for f'(x)?

To solve for f'(x), you can use the rules of differentiation such as the power rule, product rule, quotient rule, and chain rule. These rules allow you to find the derivative of a given function.

Why is f'(x) important in calculus?

f'(x) is important in calculus because it allows us to understand the behavior of a function and its rate of change. It also helps us find maximum and minimum points of a function, which are crucial in optimization problems.

What does f'(x) tell us about a function?

f'(x) tells us about the slope of the tangent line to the function at a specific point x. It also indicates whether the function is increasing or decreasing at that point.

Can f'(x) be negative?

Yes, f'(x) can be negative if the function is decreasing at a specific point x. In this case, the tangent line will have a negative slope, indicating a downward trend in the function.

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