If \(f(x) = e^x g(x)\), \(g(0) = 2\), \(g'(0) = 1\) then \(f'(0)\) is equal to:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3
By the product rule:
\(f'(x) = e^x g(x) + e^x g'(x)\)
Putting x = 0, with \(e^0 = 1\):
\(f'(0) = g(0) + g'(0)\)
\(f'(0) = 2 + 1 = 3\)