AP EAMCET201823 Apr 2018Evening ShiftMathematicsDifferentiationActual
If a>0 and f(x)= ( a+x 1+x )^ a+1+2 x , then f^ (0)=
Options
- Aa^ a+1
- Ba^ a+1 1-a^2 a +2 a
- C2 a
- Da^ a+1 (1+a)^2 a-2 a
Correct answer
B. a^ a+1 1-a^2 a +2 a
Step-by-step solution
Given function, for a>0 aligned & f(x)= ( a+x 1+x )^ a+1+2 x f(0)=a^ a+1 & f(x)=(a+1+2 x) ( a+x 1+x ) aligned On differentiating both side with respect to ' x ', we are getting aligned & f^ (x) f(x) =2 ( a+x 1+x )+(a+1+2 x) 1 a+x - 1 1+x & So, f^ (0)=f(0) [2 (a)+(a+1) ( 1 a -1 ) ] & f(0)=a^ a+1 aligned So, f^ (0)=a^ a+1 1-a^2 a +2 a .