Use the rules 𝑑 𝑑𝑥 sin (𝑥) = cos(𝑥) and 𝑑 𝑑𝑥 sin (𝑓(𝑥)) = 𝑓′(𝑥) cos(𝑓(𝑥)).

If f(x) = sin(5x), determine the value of f'(π/6).

A particle moves along a straight line such that its displacement from the origin at time \(t\) seconds is given by \(s(t) = 8\sin(3t^2 + 2)\) metres, where \(t \geq 0\). (a) Use differentiation to determine an expression for the velocity \(v(t)\) of the particle at time \(t\). [2 marks] (b) Use the result from part (a) to calculate the velocity of the particle when \(t = 1.5\) seconds. Give your answer correct to two decimal places. [2 marks]

Find the derivative of $f(x) = \sin(3x)$ with respect to $x$.