1. If sin y = x sin(a + y), prove that dy = sin2(a + y)
dx siny
2. Differentiate sin–1Öx w.r.t. x using first principle.
3. If x = et (cos t + sin t) and y = et(cos t – sin t), find dy/dx at t = π/4
4. Differentiate log tan (π/4 + x/2) w.r.t. x.
5. Differentiate y = sin–1{xÖ1 – x – Öx Ö1 – x2} w.r.t. x
6. If y = sin (m sin–1x), prove that (1 – x2)y2 – xy1 + m2y = 0.
7. Differentiate eÖtan x w.r.t. x using first principle.
8. Differentiate y = (sinx)tanx +(cosx)secx
9. If x =a(cosq + qsinq), y =a(sinq – qcosq), show aq d2y/dq2 = sec3q.
