A community for students.
Here's the question you clicked on:
 0 viewing
dudeperuvian
 3 years ago
help me find dy if if y=xlnx then dy=
dudeperuvian
 3 years ago
help me find dy if if y=xlnx then dy=

This Question is Closed

vf321
 3 years ago
Best ResponseYou've already chosen the best response.2Product rule. \[f(x)=x\]\[g(x)=ln(x)\]\[y=f(x)g(x)\]\[dy=(f'(x)g(x)+f(x)g'(x))dx\]

mtaOS
 3 years ago
Best ResponseYou've already chosen the best response.0Yes It seems you will have to use the integration by parts. @vf321 is correctr.

dudeperuvian
 3 years ago
Best ResponseYou've already chosen the best response.0so it would be (x+lnx)dx ? :3

vf321
 3 years ago
Best ResponseYou've already chosen the best response.2NO! I made up some functions, f(x) and g(x). Can you tell me what they are? (Hint: Look up). Then find f'(x) and g'(x).

mtaOS
 3 years ago
Best ResponseYou've already chosen the best response.0You have to choose which one you integerate and which one you derive.

vf321
 3 years ago
Best ResponseYou've already chosen the best response.2no... Let's look at it one at a time. What is f(x)?

dudeperuvian
 3 years ago
Best ResponseYou've already chosen the best response.0f(x)= x so f' is equal to one. i get that, but how to derive lnx ;S

dudeperuvian
 3 years ago
Best ResponseYou've already chosen the best response.0thats how i got 1lnx+x(...)

vf321
 3 years ago
Best ResponseYou've already chosen the best response.2That's a definition. d/dx(lnx) = 1/x

vf321
 3 years ago
Best ResponseYou've already chosen the best response.2so now plug into the product rule: \[dy = (f(x)g'(x) + f'(x)g(x))dx\]

dudeperuvian
 3 years ago
Best ResponseYou've already chosen the best response.0\[ \frac{ lnx+x }{ x}\]

PhoenixFire
 3 years ago
Best ResponseYou've already chosen the best response.1\[f(x) = x\] \[f^{\prime}(x) = 1\] \[g(x) = \ln(x)\] \[g^{\prime}(x) = {1 \over x}\] Product rule: \[{{\delta fg}\over{\delta y}} = f^{\prime}g + fg^{\prime}\] Now substitute the equations calculated above. \[{\delta y \over \delta x} = 1\ln(x) + x{1 \over x}\] \[{\delta y \over \delta x} = \ln(x) + 1\] the x * 1/x is the same as x/x, which is the same as 1.
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.