Reverse Chain Rule How do you integrate (ax + b)n? The reverse chain rule can be used for integrating functions in the form y = (ax + b)n Make sure you are confident using the chain rule to differe...
Definite Integration What is definite integration? Definite Integration occurs in an alternative version of the Fundamental Theorem of Calculus This version of the Theorem is the one referred to by...
Integrating Powers of x What is integration? Integration is the inverse ('opposite') of differentiation How do I integrate powers of x? For each term … … increase the power (of x) by 1 … divide b...
Fundamental Theorem of Calculus What is the fundamental theorem of calculus? The Fundamental Theorem of Calculus states that integration is the inverse process of differentiation This form of the T...
Connected Rates of Change What are connected rates of change? In situations involving more than two variables you can use the chain rule to connect multiple rates of change into a single equation E...
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...
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 ...
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...
Chain Rule What is the chain rule? If y is a function of u, and u is a function of x, then the chain rule tells us that The chain rule allows us to differentiate more complicated expressions and c...
