Question
Asked Oct 13, 2019
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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)= (x2-1)/(2x-3)

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Expert Answer

Step 1

We need to find the derivative of the given function.

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d dx | 2х — 3 By Quotient rule, we know that, f'g-fg g2 d (f dx (x? — 1)°(2х — 3) — (х? — 1)(2х — 3)' d (x2 = dx2x 3 (2х — 3)2

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Step 2

Now,

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(x? — 1)' %3D 2х [using (x")' %3 пх"-1] = [using (x") 3D пх"-1] (2х — 3)' 3 2 2x (2х — 3) — (x? — 1): 2 x2 d 1 = dx 2х — 3 (2х — 3)? 4x2 — 6х — 2x2 + 2 (2х — 3)2 2x2 — бх + 2 (2х — 3)2 Н- 2x2 — бх + 2 d x2 1 dx 2х — 3 (2х — 3)?

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Calculus

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