Given,

f(x) =

⇒ f(x) =

⇒ f(x) = x² – 2x + x ^{– 1} – 2x ^{– 2}

we need to find f’(x), so differentiating both sides with respect to x –

∴

Using algebra of derivatives –

⇒ f’(x) =

Use the formula:

∴ f’(x) = 2x^{2 – 1} + 2x^{1 – 1} + ( – 1)x ^{– 1 – 1} – 2( – 2)x ^{– 2 – 1}

⇒ f’(x) = 2x + 2x⁰ – 1x ^{– 2} + 4x ^{– 3}

∴ f’(x) = 2x + 2 – x ^{– 2} + 4x ^{– 3}