A physicist models the intensity of radiation, III, at a distance x x\,x metres from a point source using the equation
I=25x3+0.4x,x≥1 I = \frac{25}{x^3} + 0.4^x, \quad x \ge 1 I=x325+0.4x,x≥1Find an expression for the rate of change of radiation intensity with respect to distance, dIdx\dfrac{dI}{dx}dxdI.
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.