Katie and Sarah are working on taking the derivative of f(x)

Last updated: 7/10/2022

Katie and Sarah are working on taking the derivative of f(x) = - 2x 3x + 4 Katie uses the quotient rule to get f'(x) = product rule and the chain rule (shown below). Explain the discrepancies between the two answers. -1 f(x) = 2x(3x+4)=1 f'(x) = 2x(-1)(3x+4)=2(3)+2(3x+4)-1 1 -2 = 2(3x + 4)¯¹ - 6x(3x+4) −² (3x+4)2-2x(3) (3x+4)² 8 (3x+4)² Sarah converts it into a Choose the correct answer below. O A. In the first answer, using the quotient rule, the exponent in the denominator is positive. Whereas, in the second answer, using the product rule and the chain rule, the exponents are negative and contain two terms. The two methods produce similar expressions. OB. In the first answer, using the quotient rule, the exponent in the denominator is positive. Also, in the second answer, using the product rule and the chain rule, the exponents are negative. The two methods produce different expressions that are not equivalent. OC. In the first answer, using the quotient rule, the exponent in the denominator is positive. Whereas, in the second answer, using the product rule and the chain rule, the exponents are negative and contain two terms. The answers are equivalent, just in different forms.