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प्रश्न
If y = cos–1 x, Find `(d^2y)/dx^2` in terms of y alone.
उत्तर
Given, y = cos-1 x
⇒ x = cos y
Differentiating both sides with respect to x,
`d/dx (x) = d/dx cos y`
or `1 = - sin y dy/dx`
`=> dy/dx = - 1/sin y = - cosec y`
Differentiating both sides again with respect to x,
`(d^2 y)/dx^2 = - d/dx` cosec y = - (- cosec y cot y) `dy/dx`
= cosec y cot y (- cosec y) ...`[dy/dx` substituting the value of]
= - cosec2 y cot y
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