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lovesit2x
Group Title
Differentiate y = e^(4x) cos x with respect to x
dy/dx = ?
 one year ago
 one year ago
lovesit2x Group Title
Differentiate y = e^(4x) cos x with respect to x dy/dx = ?
 one year ago
 one year ago

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

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

zepdrix Group TitleBest 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

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

lovesit2x Group TitleBest ResponseYou've already chosen the best response.0
wait sinx
 one year ago

zepdrix Group TitleBest 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

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

zepdrix Group TitleBest 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

zepdrix Group TitleBest 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

zepdrix Group TitleBest 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

zepdrix Group TitleBest 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

lovesit2x Group TitleBest ResponseYou've already chosen the best response.0
WOW...you just made math fun. lol Thanks
 one year ago

lovesit2x Group TitleBest ResponseYou've already chosen the best response.0
wait...its with respect to x
 one year ago
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