Question

what is the derivative of f(x)= 3cos^2 (x)

Answer 1

chain rule is works
f(x) = 3cos^2 (x)
f ' (x) = 3 * 2 cos(x) * (-sin(x)
f ' (x) = -3 * 2 cos(x) * sin(x)
if you want simplify again, use the identity
2 cos(x) * sin(x) = sin(2x)
so,
f ' (x) = -3sin(2x)

Answer 2

how did you get 2 cos(x) * (-sin(x)???

Answer 3

derivative of (..)^2 = 2(...)
derivative of cos(x) is -sin(x)
that's called the chain rule

Answer 4

is there a rule for that?

Answer 5

yes, of course
but you can use other methode if you want

Answer 6

could you please show me?

Answer 7

just use the identity :
cos^2 x = (1+cos2x)/2

Answer 8

f(x)= 3cos^2 (x)
f(x)= 3(1+cos2x)/2
f(x) = 3/2(1+cos2x)
f(x) = 3/2 + 3/2 cos2x

now derive above

Answer 9

derivative of 3/2 is 0
derivative of 3/2 cos(2x) is 3/2 * -2sin(2x) = -3sin(2x)
so, f ' = 0 + -3sin(2x) = -3sin(2x)

Answer 10

got it ?

Answer 11

ill better have to write these down so that i can get a better picture

Answer 12

thanks a lot. i got it now

Answer 13

welcome