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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,`
`"or "x=cos y`
Differentiating w.r.t. y, we get
`(dx)/(dy)=-sin y`
`"or "(dy)/(dx)=-cosec y`
Differentiating w.r.t. x, we get
`(d^(2)y)/(dx^(2))=(d)/(dx)(-cosec y)`
`=(d)/(dy)=(-"cosec "y)(dy)/(dx)`
`="cosec y cot y (-cosec y)"`
`-cot ycdot cosec^(2) y`
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