BITSAT2009MathematicsMathematical ReasoningActual
If (f(t)= 1-t 1+t ), then (f^ (1 / t) ) is equal to
Options
- A( 1 (1+t)^2 )
- B( 1 (t-1)^2 )
- C( -2 t^2 (t+1)^2 )
- D( 2 (t-1)^2 )
Correct answer
C. ( -2 t^2 (t+1)^2 )
Step-by-step solution
( aligned & f^ (t)= d d t [ 1-t 1+t ]= (1+t)(-1)-(1-t) (1) (1+t)^2 & = -1-t-1+t (1+t)^2 = -2 (1+t)^2 aligned ) (f^ [1 / t]= -2 (1+ 1 t )^2 = -2 t^2 (t+1)^2 )