Find derivatives, domains for f(x) = x + sqrt(x), f(x) = ...

[bballj228]

Find the derivative. State the domain of the function and the domain of its derivative.

1: f(x) = x + ?x

2: f(x) = (3 + x) / 1-3x

Find F'(a)

3: f(x) = (x^2 + 1) / (x - 2)

4: f(x) = ?3x + 1

 

[Deleted member 4993]

Find the derivative. State the domain of the function and the domain of its derivative.

1: f(x) = x + ?x

2: f(x) = (3 + x) / 1-3x

Find F'(a)

3: f(x) = (x^2 + 1) / (x - 2)

4: f(x) = ?3x + 1

Please show us your work and thoughts so that we know where to begin to help you.

 

[bballj228]

For the first one i got up to x + ?x = x^1/2 = x^3/2

2nd one 1(1-3x) - (-3)(3 + x) all over (1-3x)^2 = 10 / (1 - 3x) ^2

3rd one i know its the quotient rule but not sure where to go with this one

For the fourth i tried the chain rule

?3x + 1 = 3x^1/2 + 1 = 1/2(3x)^1/2

 

[stapel]

For the first one i got up to x + ?x = x^1/2 = x^3/2

How did you arrive at the conclusion that x[sup:38eapo7m]1/2[/sup:38eapo7m] somehow equalled x[sup:38eapo7m]3/2[/sup:38eapo7m]...? :shock:

2nd one 1(1-3x) - (-3)(3 + x) all over (1-3x)^2 = 10 / (1 - 3x) ^2

I will guess that the above means that "My derivative for the second function is..." as posted. If so, then your derivative expression is correct, but remember to format your answer intelligently before you hand it in. :wink:

3rd one i know its the quotient rule but not sure where to go with this one

I will guess that the above means that "I am fairly certain that finding the answer to Exercise (3) involves using the Quotient Rule, but I'm not sure how to do this."...?

You don't state how the function F(x) might relate to f(x), or how the derivative of F at x = a relates, so it is difficult to proceed. Since you applied the Quotient Rule in Exercise (2), obviously you know how to apply it to a rational function, so the difficulty must lie elsewhere, perhaps in the information (noted) which was omitted...?

For the fourth i tried the chain rule

?3x + 1 = 3x^1/2 + 1 = 1/2(3x)^1/2

I'm sorry, but I can't make heads or tails of this...? In addition to the missing information regarding F(x), f(x), and x = a, your string of "equalities" makes no sense. You have the function:

. . . . .\(\displaystyle f(x)\, =\, \sqrt{3}\, x \, +\, 1\)

Somehow, you ended up with:

. . . . .\(\displaystyle \sqrt{3}\, x \, +\, 1\, =\, 3\sqrt{x}\, +\, 1\, =\, \frac{1}{2} \sqrt{3x}\)

...which is obviously nonsense.

Please reply with the missing information, along with a clear listing of your work and reasoning so far. This would include numbering, complete sentences, and explanations for your "equals" that aren't actually.

Thank you!

Eliz.

 

[bballj228]

Re:

For the first one i got up to x + ?x = x^1/2 = x^3/2

How did you arrive at the conclusion that x[sup:2rqzcmik]1/2[/sup:2rqzcmik] somehow equalled x[sup:2rqzcmik]3/2[/sup:2rqzcmik]...? :shock:

i tried it again is this it? x^(1/2)+x^1=x^(1/2)*(1+x^(1/2))

and for number 4 i really don't know how i got that so it would be nice if you can help me and explain what to do as i am obviously lost.

 

[stapel]

i tried it again is this it? x^(1/2)+x^1=x^(1/2)*(1+x^(1/2))

I will guess that the "it" is the derivative of the function given in Exercise (1); namely, f(x) = x + sqrt[x]. However, I don't understand the motivation for what you've done here...?

You appear to have "factored" the function, to get sqrt[x](sqrt[x] + 1). While this is equal to the original function, it of course only complicates the process of finding the derivative. :shock:

Are the posted instructions incorrect? Are you supposed to be doing something other than differentiating? If you are supposed to be differentiating, what is the reasoning behind "factoring" first? (I don't know what esoteric "method" your text may be using. You may have a very good reason for whatever it is that you're doing, but it really would help if you'd tell us what's going on. I'm sorry, but that's really the only way we can know.) :!:

for number 4 i really don't know how i got that so it would be nice if you can help me and explain what to do as i am obviously lost.

As previously mentioned, until you provide at least the relationship between F(x) and f(x), it is impossible for us to advise, since we have no way of knowing how the derivative of F(x) at x = a might relate to the given function, f(x). Also, since you have stated three different (and mutually exclusive) forms for "f(x)", we can't even know with what function or functions you're needing to work. :?:

It really would help if you would state, clearly, what the functions are, what the questions are, what the instructions are, what the relationships are, and what your work and reasoning has been so far. :idea:

Please be complete. Thank you!

Eliz.