AP EAMCET202119 Aug 2021Morning ShiftMathematicsDifferentiationActual
f ( x ) = x 2 + 1 ; g ( x ) = x + 1 x 2 + 1 ; h ( x ) = 2 x - 3 . Then the value of f ' h ' g ' ( x ) =
Options
- A5
- B2 5
- C5 2
- D1 5
Correct answer
B. 2 5
Step-by-step solution
Given that f ( x ) = x 2 + 1 ; g ( x ) = x + 1 x 2 + 1 ; h ( x ) = 2 x - 3 By using Chain rule f ' x   =   2 x 2 x 2 + 1   =   x x 2 + 1 By using Quotient rule g ' x   =   x 2 + 1 1 - x 2 x x 2 + 1 2   =   x 3 - 2 x 2 + 1 x 2 + 1 2 h ' x   =   2 f ' h ' g ' x   =   f ' h ' x 3 - 2 x 2 + 1 x 2 + 1 2 = f ' 2 = 2 2 2 + 1   =   2 5