Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

zepdrixBest ResponseYou've already chosen the best response.1
Hmm looks like we'll have to apply the product rule :)
 one year ago

XavierBest ResponseYou've already chosen the best response.0
You have a product so use the product rule
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
\[\large y=e^{4x}\cos x\]\[\large y'=\color{royalblue}{\left(e^{4x}\right)'}\cos x+e^{4x}\color{royalblue}{\left(\cos x\right)'}\] Understand the setup for Product Rule? We have to take the derivative of the blue terms.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
So what's the derivative of cos x? :)
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Yes good c:\[\large y'=\color{royalblue}{\left(e^{4x}\right)'}\cos x+e^{4x}\left(\sin x\right)\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Do you remember the derivative of \(\huge e^x\) ?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Oooo tsk tsk! That's a fun easy one that you'll want to remember! c: \[\huge \left(e^x\right)'=e^x\] It gives us the same thing back. This same thing will happen in our problem here, except we'll have an extra step. Since our exponent is more than just \(\large x\), we have to apply the chain rule. Multiply the result by the derivative of the exponent. \[\huge \left(e^{4x}\right)'=e^{4x}\left(4x\right)'\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Hmm so what is the derivative of that exponent. The derivative of \(\large 4x\).... hmmmm
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
The derivative of 4x is 4x? Hmm no that's not going to work :c
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Yessss good :) Giving us, \(\huge e^{4x}(4)\) Which gives us an answer of,\[\huge y'=4e^{4x}\cos x+e^{4x}\left(\sin x\right)\]
 one year ago

lovesit2xBest ResponseYou've already chosen the best response.0
WOW...you just made math fun. lol Thanks
 one year ago

lovesit2xBest ResponseYou've already chosen the best response.0
wait...its with respect to x
 one year ago
See more questions >>>
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.