We need to find the derivative of f(x) = (x² + 1)(x – 5)

Derivative of a function f(x) from first principle is given by –

f’(x) = {where h is a very small positive number}

∴ derivative of f(x) = (x² + 1)(x – 5) is given as –

f’(x) =

⇒ f’(x) =

⇒ f’(x) =

Using (a + b)² = a² + 2ab + b² and (a + b)³ = a³ + 3ab(a + b) + b³ we have –

⇒ f’(x) =

⇒ f’(x) =

Take h common –

⇒ f’(x) =

As h is cancelled, so there is no more indeterminate form possible if we put value of h = 0

∴ f’(x) =

So, evaluate the limit by putting h = 0

⇒ f’(x) = 3x² + 3(0)x + 0² + 1 – 10x – 5(0)

⇒ f’(x) = 3x² – 10x + 1

Hence,

Derivative of f(x) = (x² + 1)(x – 5) is 3x² – 10x + 1