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 ...
