If , prove that:

Given,

y =

We need to prove:

As, y = ….equation 1

Now, differentiating both sides w.r.t x –

∴ )

Using algebra of derivatives –

⇒

Use:

∴

⇒

⇒

Multiplying x both sides –

⇒

⇒

Now, multiplying y both sides –

⇒

⇒ {from equation 1}

Using (a + b)(a – b) = a² – b²

⇒

⇒