This page lists recommended resources for teaching Pure Mathematics in Year 12 (based on the 2017 A level specification), categorised by topic. Consider the straight line y = 3x + 2 shown … The power rule: To […] Example. (a) Given that , show from first principles that [5] (b) Differentiate with respect to x. Khan Academy has a really good Introduction to Differential Calculus video about Usain Bolt and instantaneous rates of change. Finding the derivative of. Selection of Videos on Introduction to Derivatives - Slope & Slope of Tangent Lines (Khan Academy) Video on Sketching Derivatives (PatrickJMT) Selection of Videos on Visualizing Derivatives (Khan Academy) Video on Finding Derivatives using the Definition (PatrickJMT) Notes & Videos on Differentiating from First Principles (mathcentre) Find the derivative of #cscx# from first principles? Math Centre Lamar: Khan Academy: 2 / 5: Quotient rule: In this section we see how to differentiate the ratio of two functions. Differentiation. These include the constant rule, power rule, constant multiple rule, sum rule, and difference rule. f (x) = 5 is a horizontal line with a slope of zero, and thus its derivative is also zero. Differentiating a linear function A straight line has a constant gradient, or in other words, the rate of change of y with respect to x is a constant. Differentiation from First Principles. ... First Principles ... my first calculus lesson focuses on differentiation from first principles. (a) Given that , find from first principles. Suppose we have a smooth function f(x) which is represented graphically by a curve y=f(x) then we can draw a tangent to the curve at any point P.It is important to be able to calculate the slope of the tangent. Huge thanks to all individuals and organisations who share teaching resources. In this section we see how the derivatives of basic trigonometric functions are calculated from first principles. See my blog post on introducing differentiation for teaching ideas; Newton, Leibniz, and Usain Bolt - Video from Khan Academy ; Differentiation Introduction - phildb on TES ; Differentiation from first principles - SRWhitehouse on TES; Differentiation from first principles discovery - Luke Pearce; Chord investigation - Jelly Maths This is called the quotient rule. Khan Academy: 2 / 5: Differentiation of trig functions. Some differentiation rules are a snap to remember and use. If you know some standard derivatives like those of x n x^n x n and sin ⁡ x, \sin x, sin x, you could just realize that the above-obtained values are just the values of the derivatives at x = 2 x=2 x = 2 and x = a, x=a, x = a, respectively. [2] 3. Differentiating from First Principles www.naikermaths.com Differentiating from First Principles - Past Exam Questions 1. We would like to find ways to compute derivatives without explicitly using the definition of the derivative as the limit of a difference quotient. 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