1.77: Chain rule and related rates

0606/13/O/N/18 — Question 4 · 6 marks

In this question, the units of xx are radians and the units of yy are centimetres.
It is given that y=(1+cos⁡3x)10y = (1 + \cos 3x)^{10}.
(i)
Find the value of dydx\dfrac{\mathrm{d}y}{\mathrm{d}x} when x=π2x = \dfrac{\pi}{2}.
[4]
(ii)
Given also that yy is increasing at a rate of 66 cm s−1^{-1} when x=π2x = \dfrac{\pi}{2}, find the corresponding rate of change of xx.
[2]