derivative of 2ln(secx)

Answer:[tex]\displaystyle \frac{dy}{dx} = 2 \tan (x)[/tex]General Formulas and Concepts:CalculusDifferentiationDerivativesDerivative NotationDerivative Property [Multiplied Constant]:                                                          [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(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 = 2 \ln (\sec x)[/tex]Step 2: DifferentiateLogarithmic Differentiation [Chain Rule, Multiplied Constant]:                   [tex]\displaystyle \frac{dy}{dx} = 2 \bigg( \frac{1}{\sec x} \bigg) \cdot \frac{d}{dx}[\sec x][/tex]Trigonometric Differentiation:                                                                       [tex]\displaystyle \frac{dy}{dx} = 2 \bigg( \frac{1}{\sec x} \bigg) \cdot \sec x \tan x[/tex]Simplify:                                                                                                         [tex]\displaystyle \frac{dy}{dx} = 2 \tan (x)[/tex] Topic: AP Calculus AB/BC (Calculus I/I + II)Unit: Differentiation