Question

derivative of f(x)= cos(x) sin(3x)

Answer 1

Derivative of function of type (UV)
Is (U'V+V'U)
Where U and V are two different function.

Answer 2

Here U=cos x
V=sin 3x
Can you tell what are U' and V'

Answer 3

U' = -sinx
V' = cos3x

Answer 4

Finding the derivative of V=sin 3x requires use of the Chain Rule. Focus carefully on that 3x. It's true that the derivative of v=sin x is v' cos x.

Answer 5

V'= 3xcos(3x)

Answer 6

not quite,

what is the derivative of 3x?

Answer 7

I did it a different way and messed up. Whoops.
it should be 3cos(3x)

Answer 8

that's better

Answer 9

so you have
U = cos x , U' = -sin x
V = sin 3x , V' = 3cos 3x

plug these into
(UV)' = (U'V+V'U)

Answer 10

(UV)' = -sin^2(3x^2) + 3cos^2(3x^2)

Answer 11

@gingycreamsicle is this correct
Can (sin a)(sin b)=sin^2 (ab) ???