What you’ll learn4 learning objectivesChoose one objective for a focused lesson, or study the complete topic.1.7.1Gradient as limit• understand the gradient of a curve at a point as the limit of the gradients of a suitable sequence of chords, and use the notations f ′(x), f ″(x), d d x y, and d d x y 2 2 for first and second derivatives Only an informal understanding of the idea of a limit is expected. e.g. includes consideration of the gradient of the chord joining the points with x coordinates 2 and (2 + h) on the curve y = x3. Formal use of the general method of differentiation from first principles is not required.Syllabus objective1.7.2Differentiation rules• use the derivative of xn (for any rational n), together with constant multiples, sums and differences of functions, and of composite functions using the chain rule e.g. find x y d d, given yx 253= +.Syllabus objective1.7.3Differentiation applications• apply differentiation to gradients, tangents and normals, increasing and decreasing functions and rates of change Including connected rates of change, e.g. given the rate of increase of the radius of a circle, find the rate of increase of the area for a specific value of one of the variables.Syllabus objective1.7.4Stationary points• locate stationary points and determine their nature, and use information about stationary points in sketching graphs. Including use of the second derivative for identifying maxima and minima; alternatives may be used in questions where no method is specified. Knowledge of points of inflexion is not included.Syllabus objective