Target Mathematics

3.96: Related rates with a tangent function

0606/22/M/J/23 — Question 4 · 6 marks

Variables xx and yy are related by y=tan(x+2)1y = \tan(x + 2) - 1 where 0xπ20 \leqslant x \leqslant \dfrac{\pi}{2}. Given that xx is increasing at a constant rate of 0.040.04 radians per second, find the corresponding rate of change of yy when y=3y = 3.
[6]