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| reminders | Content (theory) | Derivatives of expressions in secondary sch | Rules of differentiation | New differentiations to memorise/learn | Implicit differentiation example | differentiation of parametric equations | Questions (theory) | Differentiation of standard functions | Differentiate y=x^(xy) to get dy/dx in terms of x and y, and find the eqn of vertical asymptote | a certain CAM software is designed to move the nozzle along the path c described by the parametric equations x-sin^3(0), y=cos^3(0)-2. find ^2y/dx^2 in terms of → (4) | Content (applications) | Monoticity and concavity | Stationary points | Tangents and Normals | Maximization and minimization | AJC/2010/1/4: The curve C is given by the equation y=x(1/(x)^0.5) where x 0. the variable point P moves along the x-axis from x-10 to x-1 at a constant rate of 1 unit per second. Another variable point Q moves along the curve C so that the x-coordinate of both P and Q are the same at any point in time. (a) find dy/dx in terms of x. Anhd if the area of the triangle OPQ is represented by A. Show that the rate of change of A is (1/2)In(2)-3/2 | HCL/2011/1/Q3x-(u)*0.5 and y-(1/u^2)-2u. (0) Find dy/dx in terms of u. (ii) The tangent at x-1 intersects the X and Y axis at A and C respectively. Find the equation of the. Meanwhile, the normal at x-1 intersects the X and Y axis at B and D. Prove that AB-CD. (iii) and then given that u is increasing at a rate of 0.5 units per second, find the rate at which dy/dx is decreasing when u=2"}]},"collapsedThumbnail":{"thumbnails":[{"url":"https://www.youtube.com/watch?v=xRqrVrt4SU4" frameborder="0" allowfullscreen title="3 years ago (c) by youtube.com" style="float:{#vleft left|#vleft left|#vleft left|#vleft left|#vright right};padding:{#vright 10px 0px 10px 10px|#vleft 10px 10px 10px 0px};border:0px;"></iframe>

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