A robotic arm's torque τ\tauτ (in Newton-metres) during a specific maneuver is modeled as a function of the joint angle θ\thetaθ (in radians) by:
τ(θ)=4θ3+5θsinθ,0<θ<π \tau(\theta) = \frac{4\theta^3 + 5\theta}{\sin \theta}, \quad 0 < \theta < \pi τ(θ)=sinθ4θ3+5θ,0<θ<πFind an expression for the rate of change of torque with respect to the angle, dτdθ\displaystyle \frac{d\tau}{d\theta}dθdτ.
109 exam-style questions on CCEA A Level Maths 3.5.2 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.