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NDA2018MathematicsContinuity and DifferentiabilityActual

Let f(x+y)=f(x) f(y) and f(x)=1+x g(x) (x) , where _ x 0 g(x)=a and _ x 0 (x)=b . Then what is f^ (x) equal to?

Options

  1. A1+ abf ( x )
  2. B1+ ab
  3. Cab
  4. Dabf ( x )

Correct answer

D. abf ( x )

Step-by-step solution

aligned & f^ (x) & _ h 0 f(x+h)-f(x) h = _ h 0 f(x) f(h)-f(x) h & = _ h 0 f(x)[f(h)-1] h = _ h 0 f(x)[h g(h) (h)] h & =a b f(x) aligned

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