Correct Answer - Option 2 : 2x
Calculation:
f\(\rm \left(x+{1\over x}\right)\) = x2 + \(\rm 1\over x^2\)
f\(\rm \left(x+{1\over x}\right)\) = x2 + \(\rm 1\over x^2\) + 2 - 2
f\(\rm \left(x+{1\over x}\right)\) = \(\rm \left(x + {1\over x}\right)^2\) - 2
Let u = \(\rm x+{1\over x}\)
f(u) = u2 - 2
f(x) = x2 - 2
Differentiating with respect to x, we get
⇒ f'(x) = 2x