Everything Maths Grade 12

CHAPTER 7. DIFFERENTIAL CALCULUS 7.4

Example 8: Rules of Differentiation

QUESTION

Determine the derivative of x− 1 using the rules of differentiation.

SOLUTION

Step 1 : Identify the rules that will be needed

We will apply two rulesof differentiation:

d

dx

(xn) = nxn−^1

and

d

dx

[f (x)−g(x)] =

d

dx

[f (x)]−

d

dx

[g(x)]

Step 2 : Determine the derivative

In our case f (x) = x and g(x) = 1.

f�(x) = 1

and

g�(x) = 0

Step 3 : Write the final answer

The derivative of x− 1 is 1 which is the same result as was obtained earlier, from

first principles.

Summary of Differentiation Rules EMCBI

Given two functions, f (x) and g(x) and constant b, n and k, we know that:

d

dxb = 0

d

dx(x

n) = nxn− 1

d

dx(kf ) = k

df

dx

d

dx(f +g) =

df

dx+

dg

dx