Given that x x\,x is measured in radians, prove, from first principles, that the derivative of sinx \sin x\,sinx is cosx\cos xcosx.
You may assume the formula for sin(A±B)\sin(A \pm B)sin(A±B), and that as h→0h \to 0h→0, sinhh→1\dfrac{\sin h}{h} \to 1hsinh→1 and cosh−1h→0\dfrac{\cos h - 1}{h} \to 0hcosh−1→0.
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.