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If f\(\rm \left(x+{1\over x}\right)\)= x2 + \(\rm 1\over x^2\), then find f'(x) is
1. x2
2. 2x
3. x2 + 2
4. x + \(\rm 1\over x\)

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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

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