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Question
If y = sin -1 `((8x)/(1 + 16x^2))`, find `(dy)/(dx)`
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Solution
y = sin-1 `((8x)/(1 + 16x^2))`
y = sin-1 `( (2(4x))/(1 + (4x)^2))`
Put 4x = tan θ `therefore` = tan-1 (4x)
y = sin-1 `((2 tan θ)/(1 + tan^2 θ))`
y = sin-1 (sin 2θ)
y = 2θ
y = 2 tan-1 (4x)
`(dy)/(dx) = 2/(1 + (4x^2)` . 4
`(dy)/(dx) = 8/(1 + 16x^2)`
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