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JEE Main20246 Apr 2024Evening ShiftMathematicsDifferentiationActual

Suppose for a differentiable function h, h(0)=0, h(1)=1 and h^ (0)=h^ (1)=2 . If g (x)=h ( e ^x ) e ^ h(x) , then g^ (0) is equal to:

Options

  1. A5
  2. B4
  3. C8
  4. D3

Correct answer

B. 4

Step-by-step solution

aligned & g(x)=h (e^x ) e^ h(x) & g^ (x)=h (e^x ) e^ h(x) h^ (x)+e^ h(x) h^ (e^x ) e^x & g^ (0)=h(1) e^ h(0) h^ (0)+e^ h(0) h^ (1) & =2+2=4 aligned

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