Question

How can I solve? `y= 6cos2x` find `y^((6))`

calculus

Answer 1

`y^((6)) = -384 cos(2x)`

Explanation:

The sixth derivative of `y` can be found with simple repeated use of chain rule:
`y = 6 cos(2x)`
`y'=-12sin(2x)`
`y'' = -24cos(2x)`
`y''' = 48sin(2x)`
`y^((4)) = 96 cos(2x)`
`y^((5)) = -192 sin(2x)`
`y^((6)) = -384 cos(2x)`

Remembering how to differentiate sinusoids like this is a very useful skill!