A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
Given that f(x)=2h(x)+(2x/h(x)); h(4)=4, h'(4)=2. Find f'(4)
anonymous
 3 years ago
Given that f(x)=2h(x)+(2x/h(x)); h(4)=4, h'(4)=2. Find f'(4)

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0well their is: a)13/2 b)7/2 c)5/2 d)11/2 e)17/2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I tried solving for the derivative of f(x) but I must be doing something wrong or the awnser is not there

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3So what did you get for f'?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[f'(x) = h(x) + 2h'(x)+ (\frac{ 2h(x)(2x)h(x) }{ h(x)^2 }\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3Also the answer is there. h(x) shouldn't be there. you are missing h' in your quotient

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3(2x/h)'=[(2x)'h2x(h)']/h^2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so the awnser should be 19/2

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3hmm... that isn't what I got...let me check my result.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3Oh you are still assuming h is there aren't you?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3(2h)'=2(h)'=2h' not h2h'

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0well I am plugging in everything where \[h(4)+(2h'(4)) + \frac{ (2)(h(4))(2x)(h'(4)) }{ h(4)^2 } = 4 +(2(2)) + \frac{ (2)(4)(2(4))(2) }{4^2 }= f'(4)\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3Well see I keep telling you (2h)'=2h' not h2h'

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3That first term you are putting in shouldn't be there.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Could you show me what you plugged in so I understand

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3So you don't understand why (2h)' is 2h' and not h2h'?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3I'm liking I'm using the constant multiple rule.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3(cf)'=cf' Let k(x)=cf(x) To find k'(x) we use the formal definition of derivative: \[k'(x)=\lim_{\Delta x \rightarrow 0} \frac{k(x+\Delta x)k(x)}{\Delta x}=\lim_{\Delta x \rightarrow 0} \frac{cf(x+\Delta x)cf(x)}{\Delta x}\] Note: By the distributive property ab+ac=a(b+c) \[=\lim_{\Delta x \rightarrow 0} c \frac{f(x+\Delta x)f(x)}{\Delta x} \] Note: By limit properties, we can do lim c g(x) = c lim g(x) \[=c \lim_{\Delta x \rightarrow 0} \frac{f(x+\Delta x)f(x)}{\Delta x} \] Note: By definition of derivative that above is cf'(x).

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3The constant multiple rule: k=cf k'=cf'

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3So say k=ch then k'=ch' That c means constant The constant in front of h in your problem is 2 so k=2h then k'=2h'

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So when I plug in for 2h' when h(4)=4 and h'(4)=2

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.32h'(x) x is 4. 2h'(4) 2h'(4)=2(2)=4 Now simplify your quotient and add.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Does this mean 2h'= 2(2) or 2(4)

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3[2h(x)] ' =2 [ h(x)] ' =2 h'(x) This has been what I have been saying but you wrote it as h(x)2h'(x)

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3\[\cancel{h(4)}+(2h'(4)) + \frac{ (2)(h(4))(2x)(h'(4)) }{ h(4)^2 } = \cancel{4} +(2(2)) + \frac{ (2)(4)(2(4))(2) }{4^2 }= f'(4)\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3This is what you wrote earlier I'm telling you (2h)'=2h' not h2h' do you understand now?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Oh ok Now I get what you mean by this

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3I put the marks through the bad parts.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3so you understand the constant multiple rule?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Yes I do now understand the multiple rule and the awnser is 11/2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I just didnt understand it conceptually but now that I see it plugged in and used I do now
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.