Given,

f(x) =

Using (a + b)³ = a³ + 3a²b + 3ab² + b³

⇒ f(x) =

⇒ f(x) = x^3/2 + x^1/2 + x ^{– 1/2 +} x ^{– 3/2}

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) =

⇒ f’(x) =

⇒ f’(x) =

∴ f’(x) =