f^{'''}(x)=6(x^{-2})

解

f^{^{'''}} (x) = 6 (x^{- 2})

f (x) = - 6 (x ln (x) - x) + \frac{c _{1} x ^{2}}{2} + c_{2} x + c_{3}

解答ステップ

f^{'''} (x) = 6 (x^{- 2})

解く

f^{'''} (x) = 6 x^{- 2} : f^{''} (x) = - \frac{6}{x} + c_{1}

解く

f^{''} (x) = - \frac{6}{x} + c_{1} : f^{'} (x) = - 6 ln (x) + c_{1} x + c_{2}

解く

f^{'} (x) = - 6 ln (x) + c_{1} x + c_{2} : f (x) = - 6 (x ln (x) - x) + \frac{c _{1} x ^{2}}{2} + c_{2} x + c_{3}

f (x) = - 6 (x ln (x) - x) + \frac{c _{1} x ^{2}}{2} + c_{2} x + c_{3}