Get the solution to "Derivatives of products and quotients Find the derivative..."

Madeline Lott

Answered question

2021-12-08

Derivatives of products and quotients Find the derivative of the following functions by first expanding or simplifying the expression.

g (x) = \frac{x^{2} - 1}{x - 1}

Esta Hurtado

Beginner2021-12-09Added 39 answers

Step 1
Given:

g (x) = \frac{x^{2} - 1}{x - 1}

Solution:
Taking derivative using quotient rule:

g^{'} (x) = \frac{d}{d x} (\frac{x^{2} - 1}{x - 1})

Simplify:

\frac{x^{2} - 1}{x - 1} = \frac{(x - 1) (x + 1)}{(x - 1)} = (x + 1)

Step 2
Hence,
Now differentiating the simplified expression:

g^{'} (x) = \frac{d}{d x} (x + 1)

= \frac{d}{d x} (x) + \frac{d}{d x} (1)

=1
Hence,
The derivative of :

g (x) = \frac{x^{2} - 1}{x - 1} = 1

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