Question

how do i find the derivative of y= 6cot(4x)

Answer 1

what don't you understand about the problem

Answer 2

which rule i would start with...would it be the product rule?

Answer 3

if you look at it, you can see it's basically y = c*f(x)

Answer 4

You wouldn't use the product rule because you don't have two x-containing terms being multiplied. A regular coefficient (like 6 or 4 in this case) does not require the product rule.

Answer 5

and cot can be worked with by chain rule

Answer 6

so the two terms would be 6cot and 4x..er no

Answer 7

hmm...im still not seeing it

Answer 8

think of it this way
6cot( somthing )

Answer 9

chain rule tells you 'aha i see parans, i must take the derivative of the inner function and pull it out'

Answer 10

so you metally think ok, so it should be
6 * derivative of something * cot ( something )

Answer 11

now wait, what's the derivative of cot ( ) ?

Answer 12

that is....sec(x)^2 i think

Answer 13

or no sorry i thought that said tan haha derivative of cot is cscx^2

Answer 14

-csec(x)2 actually, you can derive it out if you get confused

Answer 15

cot = cos/sin

Answer 16

yeah

Answer 17

i dunno...the ones with trig funtions always seem to throw me off

Answer 18

so now if you recall what I wrote earler, you can reason this out

Answer 19

ok...let me see here

Answer 20

6(csc^2x)cot4x ? is that close haha

Answer 21

css(x)^2 ? where did that come from

Answer 22

i took deriviative of tan cot and plugged that in there

Answer 23

cot***

Answer 24

recall that the derivative F(G) = G'F'

Answer 25

so you have somthing of the form cF(G) where c is a constant

Answer 26

hmm...haha im still a little confused

Answer 27

what are c F and G from your stated problem

Answer 28

c = 6 cot ( ? ) = F and 4x = G

Answer 29

following thus far?

Answer 30

kind of ..what do you mean by c= 6 cot (?)

Answer 31

c =6 , cot(?) = F

Answer 32

you can see that F is a shell on G correct?

Answer 33

yeah i think so

Answer 34

since F = cot ( ? ) and G= 4x F(G) = cot(4x)

Answer 35

yeah i understand that

Answer 36

if it where this alone, then what's the derivative of the inner function?

Answer 37

or simpler, what is the inner function here in cot(4x)

Answer 38

4x...right?

Answer 39

yes, and it's derivative?

Answer 40

4

Answer 41

aye

now recall that the derivative of a nested fuction (in paraens) is

derivative of something * F ( something )

Answer 42

if you remember from the previous problem, we also had to 'reduce the outer fuction' by a power as if we were treating it as a variable

Answer 43

here there is not power, but you know that it's simply just taking the derivative of the shell... in this case F ( ? ) if F ( ? ) were (x^2)^2 then the deriviate is 2x(x^2)

Answer 44

yeah i see that...i dont know why the trig function throws me off so bad

Answer 45

so in this case, what's the derivative of F ( ? ) our shell which we had as cot ( ? )

Answer 46

we got -(1/sin(x)^2) if you recall.. aka -csec(x)^2

Answer 47

cscx^2 would be der of F(?) i think

Answer 48

yes, other than losing a negative,

but gathering what we've surmised so far, then if it were just cot(4x)
you can see what the derivative of this will be?

Answer 49

uhmmm....would it be 4(-cscx^2)

Answer 50

-4 * csc(4x)^2

Answer 51

hmm okay...

Answer 52

that was just cot(4x) , we had a constant 6 so 6 * -4 * -csec(4x)^2

Answer 53

how did you get a -4

Answer 54

for the first term

Answer 55

oh, sorry, it's 4, I thought I pulled the negative off csec

Answer 56

oh okay haha

Answer 57

does it make sense though?

Answer 58

chain rule is simple once you 'see it'

Answer 59

yeah i think i understand that part, in my answer i just left that 4 out, correct?

Answer 60

haha yeah that would make sense..

Answer 61

the answer is -14csec(4x)^2

Answer 62

er 24

Answer 63

so where does -14 come from

Answer 64

ok yeah, i get that then haha

Answer 65

so...24csc(4x)^2

Answer 66

understanding is more important than pattern matching, that's why i went all long winded on ya

Answer 67

I used to be a patter matcher but that will only get you so far

Answer 68

haha no i appreciate it a lot it definitely helped me...i have a test comin up soon so its better i learn to understand these concepts rather than just memorizing those patterns haha, thanks a lot man

Answer 69

you're missing a negative, it's -12csec(4x)^2

also, i typed on my earlier example
" (x^2)^2 then the deriviate is 2x(x^2)"
it should be (x^2)^2 whose derivative is 4x(x^2)

recall that the outer shell had a power of 2, and appeared as ( ? )^2 the derivitive of the shell is 2*( ? )^1

Answer 70

er -24