A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
Find dy/dx for y=ln(5−x)^6
anonymous
 3 years ago
Find dy/dx for y=ln(5−x)^6

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[y = \ln(5x)^6\] take derivative : \[\frac{dy}{dx} = 6 \cdot \ln(5x)^5 \frac{d(5x)}{dx}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It is by chain rule.. In chain rule we are using power rule also which says : \[y = f(x)^n\] \[\frac{dy}{dx} = n \cdot f(x)^{n1} \cdot \frac{d(f(x))}{dx}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Wait, isn't that in the case that the 6th power would be to the entire thing? I thought you brought the 6 in front since lna^b=blna

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{dy}{dx} = 6 \cdot \ln(5x)^5 \frac{d(\ln(5x)}{dx} \cdot \frac{d(5x)}{dx}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ln((x5)^6) = 6ln(x5) ( 6ln(x5) ) ' = 6/(x5)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh! duh! Got it, thank you!!1

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[y = \ln(5x)^6\] \[\frac{dy}{dx} = \frac{1}{(5x)^6} \times 6 \times (5x)^5 \times (1)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It will reduce to : \[\frac{dy}{dx} = \frac{1}{(5x)}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ln((5x)^6) = 6ln(5x) ( 6ln(5x) ) ' = 6/(5x)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Forgot 6 there.. Oh God...

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{dy}{dx} = \frac{6}{(5x)}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Yes by power rule, you can bring 6 in front: \[y = 6 \cdot \ln(5x)\] Now take the derivative..

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Okay, I've got it figured out! Thank you! If you'd like to help some more I just posted another question :)
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.