Question

if f(x)= cosxsin3x, then f'(pi/6) is equal to ?

can't seem to figure this one out ...

Answer 1

Can you differentiate f(x) using the product rule?

Answer 2

well when i used the product rule i got 3cosxcos3x-sin3x(sinx)
is this correct?

Answer 3

yes.

Answer 4

you simplified smart:)

Answer 5

Looks correct to me, now sub in x=pi/6 for your answer.

Answer 6

okay yes i tried that but how do i multiply the cos 3 and pi/6 ?

Answer 7

All you have to do is 3*cos(pi/6)*cos(3pi/6)-sin(3*pi/6)sin(pi/6)
Simplifying the fractions we're left with: 3*cos(pi/6)*cos(pi/2)-sin(pi/2)sin(pi/6)

Answer 8

okay so the answer is -1/2?

Answer 9

yes, it is -1/2.
http://www.wolframalpha.com/input/?i=+3cos%28pi%2F6%29cos%28pi%2F2%29-sin%28pi%2F2%29%28sin%28pi%2F6%29%29

Answer 10

okay. thank you so much ! :)

Answer 11

Anytime, I only verified it.