<prompt> Motsoako oa x2 2x 8 ke ofe?nan  <response>: Instruction in English: What is the derivative of x2 2x 8? . Response in English: The derivative of a function gives the slope of the tangent line to the function at any point. To find the derivative of the polynomial function fx x2 2x 8, we can use the power rule, which states that the derivative of xn is n xn-1, where n is a constant.Using this rule, we can compute the derivative of each term in the given polynomial:- The derivative of x2 is 2 x2-1 2x.- The derivative of 2x is 2 x1-1 2.- The derivative of the constant term 8 is 0, since the derivative of any constant is 0.Therefore, the derivative of fx is the sum of the derivatives of each term: fx 2x 2. . Response in Sesotho: Motsoako oa tšebetso o fana ka moepa oa tangent ho ea tšebetsong ntlheng efe kapa efe. Ho fumana derivative ea polynomial function fx x2 2x 8, re ka sebelisa molao oa matla, o bolelang hore motsoako oa xn ke n xn- 1, moo n e leng kamehla. Ka ho sebelisa molao ona, re ka kopanya motsoako oa lentsoe ka leng ho polynomial e fanoeng: - Motsoako oa x2 ke 2 x2-1 2x. - Letlapa la 2x ke 2 x1-1 2. - Motsoako oa lentsoe le sa fetoheng 8 ke 0, kaha motsoako oa ntho efe kapa efe e sa fetoheng ke 0. Ka hona, tlhapi ea fx ke kakaretso ea lihlahisoa tsa lentsoe ka leng: fx 2x 2. 