If x = a (cos t + t sin t) and y = a (sin t – t cos t), findand

x = a (cos t + t sin t)

Differentiating w.r.t t-

_{We need to make use of product rule to find derivative of t sin t}

= a (-sin t +t cos t +sin t)

⇒ = at cos t ------- (i)

Again differentiating w.r.t t using product rule we get -

⇒ = a (Cos t – t Sin t)

y = a (sin t – t cos t)

Differentiating w.r.t t

_{We need to make use of product rule to find derivative of t cos t.}

= a (Cos t - t (- Sin t) - Cos t)

⇒ = a (Cos t + t Sin t – Cos t)

⇒ = at Sin t ------- (ii)

Again differentiating w.r.t t using product rule we get -

Dividing the equation (ii) by equation (i)

Differentiating w.r.t x applying chain rule-

{using equation i}

⇒