2.52: Quotient rule with sine in the denominator

0606/22/O/N/18 — Question 3 · 6 marks

A curve has equation y=x3sin2xy = \dfrac{x^{3}}{\sin 2x}. Find
(i)
dydx\dfrac{\mathrm{d}y}{\mathrm{d}x},
[3]
(ii)
the equation of the tangent to the curve at the point where x=π4x = \dfrac{\pi}{4}.
[3]