Given that x x\,x is measured in radians, prove, from first principles, that the derivative of cos(x)\cos (x)cos(x) is −sin(x)-\sin (x)−sin(x)
Using the formula for cos(A±B)\cos (A \pm B)cos(A±B) and the facts that as h→0h \rightarrow 0h→0 sinhh→1\displaystyle \frac{\sin h}{h} \rightarrow 1hsinh→1 and cosh−1h→0\displaystyle \frac{\cos h - 1}{h} \rightarrow 0hcosh−1→0, prove the result.
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.