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.
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.