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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
Fill in the Blanks
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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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