derivatives (6x)(e^5x)

Answer:[tex]\displaystyle \frac{dy}{dx} = 6e^\big{5x}(5x + 1)[/tex]General Formulas and Concepts:CalculusDifferentiationDerivativesDerivative NotationDerivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]Basic Power Rule:f(x) = cxⁿf’(x) = c·nxⁿ⁻¹  Derivative Rule [Product Rule]:                                                                             [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)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 = 6xe^\big{5x}[/tex]Step 2: DifferentiateDerivative Rule [Product Rule]:                                                                     [tex]\displaystyle y' = \frac{d}{dx}[6x]e^\big{5x} + 6x\frac{d}{dx}[e^\big{5x}][/tex]Rewrite [Derivative Property - Multiplied Constant]:                                   [tex]\displaystyle y' = 6\frac{d}{dx}[x]e^\big{5x} + 6x\frac{d}{dx}[e^\big{5x}][/tex]Basic Power Rule:                                                                                         [tex]\displaystyle y' = 6e^\big{5x} + 6x\frac{d}{dx}[e^\big{5x}][/tex]Exponential Differentiation [Derivative Rule - Chain Rule]:                       [tex]\displaystyle y' = 6e^\big{5x} + 6xe^\big{5x}\frac{d}{dx}[5x][/tex]Rewrite [Derivative Property - Multiplied Constant]:                                   [tex]\displaystyle y' = 6e^\big{5x} + 30xe^\big{5x}\frac{d}{dx}[x][/tex]Basic Power Rule:                                                                                         [tex]\displaystyle y' = 6e^\big{5x} + 30xe^\big{5x}[/tex]Factor:                                                                                                           [tex]\displaystyle y' = 6e^\big{5x}(5x + 1)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)Unit: Differentiation