"Derivatives of products and quotients Find the derivative..." was answered by our community

folklorahhe

Answered question

2021-11-25

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

h (x) = \frac{x^{3} - 6 x^{2} + 8 x}{x^{2} - 2 x}

Answer & Explanation

Cherry McCormick

Beginner2021-11-26Added 23 answers

Step 1
Given function is

h (x) = \frac{x^{3} - 6 x^{2} + 8 x}{x^{2} - 2 x}

.
First simplify the given function as follows.

h (x) = \frac{x^{3} - 6 x^{2} + 8 x}{x^{2} - 2 x}

= \frac{x (x^{2} - 6 x + 8)}{x (x - 2)}

= \frac{x (x - 2) (x - 4)}{x (x - 2)}

=x-4
Step 2
Now compute the derivative.
h'(x)=(x-4)'
=x'-(4)'
=1-0
=1

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