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If y=cos^(-1)x , find (d^2y)/(dx^2) in t...

If `y=cos^(-1)x` , find `(d^2y)/(dx^2)` in terms of `y` alone.

Text Solution

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`y="cos"^(-1)x impliesx=cos y`
`implies(dy)/(dx)= -sin y`
`implies(dy)/(dx)= -(1)/("sin"y)= -"cosec " y`
`implies (d^(2)y)/(dx^(2))=(d)/(dx)(-"cosec " y)`
`="cosec "y" cot "y*(dy)/(dx)`
`="cosec "y" cot"y(-"cosec "y)`
`= -"cosec"^(2)y" cot "y`
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