Quotient Rule What is the quotient rule? The quotient rule is a formula that allows you to differentiate a?quotient of two functions?(ie one function divided by another) If ?where?u?and?v?are funct...
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 復習筆記：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...
