Product Rule What is the product rule? The product rule is a formula that allows you to differentiate a product of two functions If where u and v are functions of x then the product rule is: In fu...
Chain Rule What is the chain rule? The chain rule is a formula that allows you to differentiate composite functions If y is a function of u, and u is a function of x, then the chain rule tells us t...
Differentiating Other Functions (Trig, ln & e etc) How do I differentiate common functions? These are the common results How do I differentiate exponentials and logarithms? The two basic differ...
First Principles Differentiation - Trigonometry How do I derive the derivatives of trigonometric functions from first principles? Recall that for a function f(x) the definition of the derivative fr...
Modelling with Differentiation inc. Optimisation How can I use differentiation to solve modelling questions? Derivatives can be calculated for any variables – not just y and x In every case the der...
Sketching Gradient Functions How can I sketch a function's gradient function? Using your knowledge of gradients and derivatives you can use the graph of a function to sketch the corresponding gradi...
Stationary Points & Turning Points What are stationary points? A stationary point is any point on a curve where the gradient is zero To find stationary points of a function f(x) Step 1: Find th...
Conduction Thermal energy transfers from hotter areas to cooler areas by the processes of: Conduction Convection Radiation Objects will always lose heat until they are in thermal equi...
Second Order Derivatives What is the second order derivative of a function? If you differentiate the derivative of a function (ie differentiate the function a second time) you get the second order ...
Edexcel IGCSE Physics: Double Science 复习笔记：4.1.3 Efficiency Efficiency The efficiency of a system is a measure of how well energy is transferred in a system Efficiency is defined as: &n...
Increasing & Decreasing Functions What are increasing and decreasing functions? A function f(x) is increasing on an interval [a, b] if f'(x) ≥ 0 for all values of x such that a< x < b. If...
Gradients, Tangents & Normals Using the derivative to find the gradient of a curve To find the gradient of a curve y= f(x) at any point on the curve, substitute the x‑coordinate of the point in...
