About the lecture

In this mini-lecture, we introduce the derivatives of common functions. In particular, we consider: (i) a table 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), along with their derivatives; (ii) alternative notation for the derivative: if y = f(x), then the derivative f’(x) can be written as dy/dx; (iii) how to use the derivative to help us find the equation for the tangent line to y = √x at x = 4; (iv) how to find the equation of the normal to the tangent just determined, which is left as an exercise; and (v) a final exercise on finding the tangent and normal to y = 2^x at x = 1.

About the lecturer

Samir Siksek is a Professor of Mathematics at the University of Warwick. His research interests include Galois representations, modularity, explicit arithmetic geometry, arithmetic of curves and surfaces, Diophantine equations (the generalized Fermat equation in particular), and Waring's problem. In 2012, he appeared on BBC Radio 4’s In Our Time program discussing Fermat’s Last Theorem.