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AP EAMCET20225 Jul 2022Morning ShiftMathematicsDifferentiationActual

If 3 f( x)+2 f( x)=5 x , then f^ ( x)+f^ ( x)=

Options

  1. A-5( x+ x)
  2. B-5 x x
  3. C-5 x - 5 x
  4. D5 x + 5 x

Correct answer

C. -5 x - 5 x

Step-by-step solution

3 f( x)+2 f( x)=5 x ...(i) 3 f( x)+2 f( x)=5 ( 2 -x ) ...(ii) Solving Eqs. (i) and (ii) simultaneously, we get f( x)=5 x- aligned & - x f^ ( x)=5 & f^ ( x)= -5 x aligned Similarly, f^ ( x)= -5 x aligned & =f^ ( x)+f^ ( x) & = -5 x - 5 x aligned

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