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If y=tan-1(x-x1+x32), then y'(1) is ______

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Question

If `y = tan^-1((sqrtx - x)/(1 + x^{3/2}))`, then y'(1) is ______ 

Options

  • 0

  • `1/2`

  • -1

  • `-1/4`

MCQ
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Solution

If `y = tan^-1((sqrtx - x)/(1 + x^{3/2}))`, then y'(1) is `underline(-1/4)`.

Explanation:

`y = tan^-1((sqrtx - x)/(1 + x^{3/2})) = tan^-1(sqrtx) - tan^-1(x)`

∴ `y^' = 1/(1 + x). 1/(2sqrtx) - 1/(1 + x^2)`

∴ `y^'(1) = 1/2. 1/2 - 1/2 = (-1)/4`

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Derivative of Inverse Functions
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