Introduction to differentiation

At the end of this chapter, you should be able to:

• state that calculus comprises two parts − differential and integral calculus • understand functional notation • describe the gradient of a curve and limiting value • differentiate y = axn by the general rule • differentiate sine and cosine functions • differentiate exponential and logarithmic functions

Calculus is a branch of mathematics involving or leading to calculations dealing with continuously varying functions such as velocity and acceleration, rates of change and maximum and minimum values of curves. Calculus has widespread applications in science and engineering and is used to solve complicated problems for which algebra alone is insufficient. Calculus is a subject that falls into two parts: (a) differential calculus (or differentiation),

(b) integral calculus (or integration). This chapter provides an introduction to differentiation and applies differentiation to rates of change. Chapter 35 introduces integration and applies it to determine areas under curves. Further applications of differentiation and integration are explored in Engineering Mathematics (Bird, 2014).