f^{''}(x)=5x^2-10x-6/(x^4)

解

f^{^{''}} (x) = 5 x^{2} - 10 x - \frac{6}{x ^{4}}

f (x) = \frac{5 x ^{4}}{12} - \frac{5 x ^{3}}{3} - \frac{1}{x ^{2}} + c_{1} x + c_{2}

解答ステップ

f^{''} (x) = 5 x^{2} - 10 x - \frac{6}{x ^{4}}

解く

f^{''} (x) = 5 x^{2} - 10 x - \frac{6}{x ^{4}} : f^{'} (x) = \frac{5 x ^{3}}{3} - 5 x^{2} + \frac{2}{x ^{3}} + c_{1}

解く

f^{'} (x) = \frac{5 x ^{3}}{3} - 5 x^{2} + \frac{2}{x ^{3}} + c_{1} : f (x) = \frac{5 x ^{4}}{12} - \frac{5 x ^{3}}{3} - \frac{1}{x ^{2}} + c_{1} x + c_{2}

f (x) = \frac{5 x ^{4}}{12} - \frac{5 x ^{3}}{3} - \frac{1}{x ^{2}} + c_{1} x + c_{2}