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...
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...
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...
First Principles Differentiation What is the derivative or gradient function? For a curve?y?=?f(x)?there is an associated function called the?derivative?or?gradient function The derivative of f(x) ...
