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.
717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.