Rational Function Definition

MathematicsFunctionsMedium

Published: April 24, 2026

Question

2 f(x) = $rac{x^2}{x-1}$

Animated Video Solution

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Step 1

Hi Precious, let's analyze this function and find its derivative step by step.

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

Step 2

To find the derivative of a function where one expression is divided by another, we use the quotient rule.

Step 3

Let's define our parts. We can set u equal to x squared and v equal to x minus one.

Let $u = x^2$ and $v = x - 1$

Step 4

Now we calculate the derivatives of these parts. The derivative of x squared is two x.

$$u' = 2x$$

Step 5

And the derivative of x minus one is simply one.

$$v' = 1$$

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