If \(f(x) = (1 + x)(1 + x^{2})(1 + x^{4})\), then the value of \(f'(1)\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 28
Multiplying out the product step by step:
\((1 + x)(1 + x^{2}) = 1 + x + x^{2} + x^{3}\)
\(f(x) = (1 + x + x^{2} + x^{3})(1 + x^{4})\)
\(= 1 + x + x^{2} + x^{3} + x^{4} + x^{5} + x^{6} + x^{7}\)
Differentiating term by term:
\(f'(x) = 1 + 2x + 3x^{2} + 4x^{3} + 5x^{4} + 6x^{5} + 7x^{6}\)
\(f'(1) = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28\)