Question

find f' for the function: f(x)= e^2xcos3x

Answer 1

Not clear what the function is. Is it\[f(x)= e^{2xcos3x}~or~f(x)= e^{2x}\cos3x\]

Answer 2

the second one. i have to use the rule (f x g)'= f' x g + f x g'

Answer 3

Correct. What do you get?

Answer 4

Make sure you use the chain rule along the way....

Answer 5

i have e^2x = 2e^2x cos 3x
but i forgot how to find (cos 3x)'
i know it becomes -sin but i dont know how to combine that with e^2x

Answer 6

I get
\[f(x)=e^{2x}\cos3x \implies f'(x)=2e^{2x}\cos3x−3e^{2x}\sin3x\]

Answer 7

the only thing i cant remember is why there is a 3 in front of e^2x sin3x

Answer 8

Chain rule I mentioned above. Function is cos(u), derivative is -sin(u) u'. In this case u'=3.

Answer 9

Came from the same place the two in front of the first term did.

Answer 10

i get it now. now to find f' of the new function, ill just use the chain rule again?

Answer 11

f=2e^2x cos3x
g=-3e^2x sin3x

Answer 12

Stated another way, let f(x) = g(x)h(x), so f'(x)= g'h(x)+gh'(x). In the current case, g(x)=e^(2x) and h(x)=cos(3x). Use the chain rule on g and h to get g'(x)=2e^(2x) and h'(x)=-3sin(3x). Assemble as indicated above to get the answer I have further above.

Answer 13

You want to find the second derivative?

Answer 14

unfortunately :-(

Answer 15

No sweat, just keep doing it again. Remember, you have two terms in the first derivative, each with two functions, so your second derivative will have four terms before simplification.

Answer 16

i like the way you explained it before using "h" and "g". its more clear somehow

Answer 17

i got: 2 [2e^(2x) cos3x-3e^(2x) sin3x] - 3[2e^(2x) sin3x + 3e^(2x) cos3x]
four terms? is that right?

Answer 18

Lets look. I get this.\[f′(x)=2e^{2x}\cos(3x)−3e^{2x}\sin(3x) \]\[\implies f"(x)=4e^{2x}\cos(3x)-6e^{2x}\sin(3x)-6e^{2x}\sin(3x)-9e^{2x}\cos(3x)\]\[=4e^{2x}\cos(3x)-12e^{2x}\sin(3x)-9e^{2x}\cos(3x)\]

Answer 19

I think our answers are equivalent.

Answer 20

These problems aren't too bad as long as you stay methodical and work them step-by-step. Pay attention to the details, and you will get a lot of right answers.

Answer 21

OMG!!! thank you so much, i feel a weight lifted lol. i was so nervous typing my answer. i want to thank you for your help, i really appreciate it. i have to go now, my moms yelling its dinner time. Thanks again!

Answer 22

No sweat.