Question
If y= ^ -1 ( x -x 1+x^ 3 2 ), then y^ (1) is equal to
BITSAT
Mathematics
Differentiation
2024
BITSAT 2024 (Memory Based Paper 3)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 0
- B. 1 2
- C. -1
- D. - 1 4
Answer
D. - 1 4
Step-by-step solution
Given, aligned y & = ^ -1 ( x -x 1+x^ 3 2 ) \\ y & = ^ -1 ( x -x 1+ x x ) \\ y & = ^ -1 ( x )- ^ -1 x \\ & [ ^ -1 ( x-y 1+x y )= ^ -1 x- ^ -1 y ] aligned Differentiating w.r.t x y^ (x)= d y d x = 1 1+x 1 2 x - 1 1+x^2 Now, y^ (1)= 1 2 1 2 - 1 2 =- 1 4
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