1.

If `y=(1)/(logcosx)`, find `(dy)/(dx).`

Answer» Given : `y=(log cos x)^(-1).`
Putting `cosx=t` and `log cos x=logt=u`, we get
`y=u^(-1)=(1)/(u),u=log t and t = cos x`
`rArr(dy)/(dx)=(-1)/(u^(2)),(du)/(dt)=(1)/(t) and (dt)/(dx)=-sinx`
`rArr(dy)/(dx)=((dy)/(dx)xx(du)/(dt)xx(dt)/(dx))`
`={(-1)/(u^(2))xx(1)/(t)xx(-sinx)}={(1)/((log cos x)^(2)).(1)/(cos x).sinx}`
`=(tanx)/((log cos x)^(2))`


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