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...
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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...
Differentiating Powers of x How do I differentiate expressions involving powers of x? Powers of x are differentiated according to the following formulae: Differentiating terms with positive integer...
Definition of Derivatives What is the derivative of a function? Differentiation is an operation that calculates the rate of change of a function with respect to a variable This means how much the ...
