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Find the derivative of the function using the definition of a derivative. State the domain of the function and the domain of its derivative.$f(x)=\frac{x^{2}-1}{2 x-3}$

domain of the function $\mathbb{R}-\left[\frac{3}{2}\right]$domain of the derivative $\mathbb{R}-\left[\frac{3}{2}\right]$

Calculus 1 / AB

Chapter 3

Derivatives

Section 2

The Derivative as a Function

Campbell University

University of Michigan - Ann Arbor

Idaho State University

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Hi. This is Claire. So in number 28 storage by calculus book. So we're gonna find the derivative using the definition in state the domain of both the original and Derby Devotion. So here already wrote the orginal equation, And I also, um, both the definition of the derivative. So what, we're gonna first do this plugging X plus eight, But the original equation. So it's gonna be cold, woman, you know, seeing each approaches. Zero next. Once square minus one over to, uh, thanks. Once beach minus three more gonna subtract up by the original equations was next square minus one over two weeks, minus three all over each. We simplify this, it's gonna become super long, so it's gonna be We'll start here when it does, each approaches. So we're gonna get two ex cute waas for that square. Each plus two x each square minus two x minus three square minus six. Next, each minus three inch square plus three minus two X cube minus two that square kinds age waas three X square plus two minutes. Wants to teach minus three. Could the all over huge Klein's q X waas to beach minus serene times two cups minus three I've only simplify this. Where can I get then? See Bones four score minus six bucks My nist to square waas too. Oh, movers two x plus three square. And then the final answer is to x square. My nose fits. What's waas to fall over too? Thanks. Waas Green Square, My box. The answer No for our derivatives The durability for our original equation It's gonna be ex can be smaller and 2/3 or x can be larger three House Because the bottom cannot be undefined Same goes for for, um no of time of eggs That's must to be smaller than three No 2/3 war no more bigger three homes

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