Consider the function .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Consider the function

g(x)=\dfrac{3x^{2}+2x-5}{x-2}

. (i) Identify the domain of

g(x)

. (ii) Find

g'(x)

and simplify your answer so that the denominator is free of common factors with the numerator. (iii) Calculate the value of

g'(5)

Related theory

Rational Functions
Differentiation Rules
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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