Derivative of y = cos(x-1)/(x-1)

Answer:[tex]\displaystyle y' = \frac{- \cos (x - 1)}{(x - 1)^2} - \frac{\sin (x - 1)}{x - 1}[/tex]General Formulas and Concepts:CalculusDifferentiationDerivativesDerivative NotationDerivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]  Basic Power Rule:f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]Step-by-step explanation:Step 1: DefineIdentify[tex]\displaystyle y = \frac{\cos (x - 1)}{x - 1}[/tex]Step 2: DifferentiateDerivative Rule [Quotient Rule]:                                                                   [tex]\displaystyle y' = \frac{\Big( \cos (x - 1) \Big)'(x - 1) - \cos (x - 1)(x - 1)'}{(x - 1)^2}[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]:                   [tex]\displaystyle y' = \frac{- \sin (x - 1)(x - 1)'(x - 1) - \cos (x - 1)(x - 1)'}{(x - 1)^2}[/tex]Basic Power Rule [Derivative Properties]:                                                   [tex]\displaystyle y' = \frac{- \sin (x - 1)(x - 1) - \cos (x - 1)}{(x - 1)^2}[/tex]Simplify:                                                                                                         [tex]\displaystyle y' = \frac{- \cos (x - 1)}{(x - 1)^2} - \frac{\sin (x - 1)}{x - 1}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)Unit: Differentiation