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Question
Find the nth derivative of the following : cos x
Solution
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 nth order derivative is given by
`(d^ny)/(dx^n) = cos((npi)/2 + x)`.
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