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NDA2017MathematicsDifferentiationActual

Let f( x + y )=f( x ) f( y ) for all x and y . Then what is f^ (5) equal to [where f^ ( x ) is the derivative of f( x ) ]?

Options

  1. Af(5) f^ 0
  2. Bf(5)-f^ (0)
  3. Cf(5) f(0)
  4. Df(5)+f^ (0)

Correct answer

A. f(5) f^ 0

Step-by-step solution

aligned & f(x+y)=f(x) f(y) & Let f(x)=a^x & f(x+y)=a^ x+y =a^x a^y=f(x) f(y) & f(5)=a^5 & f(5)=a^5 a & =f(5) f(0) & f^1(0)=a^0 a & = a aligned

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