MHT CET202016 Oct 2020Evening ShiftMathematicsDifferentiationActual
If f(x)= ⁻¹ ( 1-x 2 ) , then f^ (x)=
Options
- A-1 2 1-x²
- B1 1-x²
- C-1 2 1+x²
- D1 2 1+x²
Correct answer
A. -1 2 1-x²
Step-by-step solution
(B) d d x [ ⁻¹ ( 1-x 2 ) ]= 1 1- ( 1-x 2 )² d d x ( 1-x 2 )= 1 1- 1-x 2 1 2 1-x 2 d d x ( 1-x 2 )= 1 2-1+x 2 1 2 1-x -1 2 = 2 1+x 1 2 1-x -1 2 = -1 2 1-x² This problem can also be solved as follows array l f(x)= ⁻¹ ( 1-x 2 ) Put x= 1-x 2 = 1- 2 = 2 ² 2 2 = 2 f(x)= ⁻¹ ( 2 )= 2 = ⁻¹ x 2 f^ (x)= -1 2 1-x² array