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If y = sin^(n) x cos nx, " then" (dy)/(...

If ` y = sin^(n) x cos nx, " then" (dy)/(dx)` is

A

`n sin ^(n -1) x cos nx `

B

`n sin ^( n -1) x cos ( n +1) x `

C

`n sin ^(n -1) x sin ( n +1) x`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`y=sin^nx cos nx`
`(dy)/(dx)= cosnx (d)/(dx)sin^(n) x+ sin^(n) x(d)/(dx) cos nx `
`= nsin^(n-1)xcosnxcosx-nsin^nxsinnx`
`= nsin^(n-1)x(cosnxcosx-sinnxsinx)`
`=nsin^(n-1)xcos (nx+x)= nsin^(n-1)xcos(n+1)x`
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