Straight Lines and Gradients

Differentiation I

In this course, Professor Samir Siksek (University of Warwick) gives an introduction to differentiation for AS and A-Level students in the first of his three-course series on this topic. In the first mini-lecture, we recall the equation of a straight line and discuss gradient. In the second mini-lecture, we determine the equation for a tangent line to a curve. In the third mini-lecture, we use our work from the previous mini-lecture to define the derivative at a point on a curve as the equation for the gradient of the tangent at that point on the curve. In the fourth mini-lecture, we calculate the derivative of various basic functions from first principles. In the fifth mini-lecture, we introduce the derivatives of common functions including f(x) = c, f(x) = xⁿ, f(x) = sin(kx), f(x) = cos(kx), f(x) = e^kx, and f(x) = ln(kx).

Straight Lines and Gradients

In this mini-lecture, we recall the equation of a straight line and discuss gradient as motivation for Topic 7.1. As we move through this mini-lecture, we think about: (i) the equation of a straight line, y = mx + c, where m is the gradient and c is the y-intercept; (ii) how to find the gradient of a line passing through two given points; (iii) how the gradient is the rate of change of y with respect to x; and (iv) the equation for a line given one point on the line and the gradient.