Question

Find the n^th derivative of the following : cos x

Answer 1

Let y = cos x

Then `"dy"/"dx" = "d"/"dx"(cosx)`
= `-sinx`
= `cos(pi/2 + x)`

`(d^2y)/(dx^2) = "d"/"dx"(-sinx)`
= `-cosx`
= cos(π + x)

= `cos((2pi)/2 + x)`

`(d^3y)/(dx^3) = "d"/"dx"(-cosx)`

= `-"d"/"dx"(cosx)`
= – ( – sin x)
= sin x

= `cos((3pi)/2 + x)`
In general, the n^th order derivative is given by
`(d^ny)/(dx^n) = cos((npi)/2 + x)`.