Question

Take the derivative y=e^(3x) *(3sinx-cosx)

Answer 1

do I use the chain rule or product rule?

Answer 2

Both. :D

Answer 3

First use product rule.
And then use chain rule.

Answer 4

oh my >_<

Answer 5

ok

Answer 6

It is not very difficult. :)

Answer 7

product rule is sufficient..

Answer 8

chain rule just for differentiating e^3x

Answer 9

You have to use chain rule for e^(3x), differentiate it wrt 3x and then multiply it with 3.
That's it.

Answer 10

I agree with @AkashdeepDeb use both!
we need chain rule for the e^(3x)
and product rule for the other parts

Answer 11

f(x)=e^3x f'(x)=(e^3x)' g(x)=3sinx-cosx g'(x)=3cosx+sinx ?

Answer 12

first u can distribute the e^3x so it splits into two separate derivatives
and then you can do them one at a time
and just add them together at the end

Answer 13

I've been doing too much math in a row lol

Answer 14

and I've been helping too much in a row lol

Answer 15

both of those are good things! :)

Answer 16

anyways math is never too much, too much math is always too less.

Answer 17

wait so e^3x using chain rule

Answer 18

yes thats correct
you just need to combine them

Answer 19

my e^u is f and 3x is my g?

Answer 20

well its really just the derivative of e^3x=3e^3x

Answer 21

technically its the chain rule

Answer 22

i believe so
yes

Answer 23

ok, got the same result

Answer 24

so then I

Answer 25

(3e^3x)(3sinx-cosx)+(e^3x)(3cosx+sinx)

Answer 26

is this the next step?

Answer 27

@Miracrown @hartnn

Answer 28

yes, thats correct :)

Answer 29

factor out e^(3x) to simplify

Answer 30

great. Should/can I simplify this?

Answer 31

yes

Answer 32

e^3x [ (3)(3sinx-cosx)+(3cosx+sinx) ]

Answer 33

ah, understood. Thanks again :)

Answer 34

that can be further simplified...i hope you do that :)
and welcome ^_^

Answer 35

infact cos x term gets cancelled!

Answer 36

ok, I'm working it out

Answer 37

e^3x (10sinx)

Answer 38

absolutely correct! :)