MHT CET20239 May 2023Morning ShiftMathematicsDifferentiationActual
The derivative of f ( x) with respect to g ( x) at x= 4 , where f ^ ( 2 )=4 and g ^ (1)=2 , is
Options
- A2
- B1 2
- C2
- D1 2 2
Correct answer
C. 2
Step-by-step solution
aligned & Let y= f ( x) and z = g ( x) & d y ~d x = f ^ ( x) x x & dz d x = g ^ ( x) ^2 x & Now, d y dz = f ^ ( x) x x ~g ^ ( x) ^2 x & d y dz = f ^ ( x) x ~g ^ ( x) x & . d y d z |_ x= 4 = f^ ( 4 ) 4 g^ ( 4 ) 4 & = f ^ ( 2 ) (1) g ^ (1) 2 4 1 2 2 & = 2 & aligned