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lovesit2x
 2 years ago
Differentiate y = e^(4x) cos x with respect to x
dy/dx = ?
lovesit2x
 2 years ago
Differentiate y = e^(4x) cos x with respect to x dy/dx = ?

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zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Hmm looks like we'll have to apply the product rule :)

Xavier
 2 years ago
Best ResponseYou've already chosen the best response.0You have a product so use the product rule

zepdrix
 2 years ago
Best 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.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1So what's the derivative of cos x? :)

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

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Do you remember the derivative of \(\huge e^x\) ?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Oooo 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. \[\huge \left(e^{4x}\right)'=e^{4x}\left(4x\right)'\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Hmm so what is the derivative of that exponent. The derivative of \(\large 4x\).... hmmmm

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

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

lovesit2x
 2 years ago
Best ResponseYou've already chosen the best response.0WOW...you just made math fun. lol Thanks

lovesit2x
 2 years ago
Best ResponseYou've already chosen the best response.0wait...its with respect to x
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