derivative of f(x^{-1})f(x)= 1/5 x+5,x=6

解

\frac{d}{d x} (f (x)^{- 1}) f (x) = \frac{1}{5} x + 5, x = 6

f (x) = \frac{x ^{2} + 50 x + c _{1}}{10} x, f (x) = - \frac{x ^{2} + 50 x + c _{1}}{10} x

解答ステップ

\frac{d}{d x} ((f (x) x^{- 1}) f (x)) = \frac{1}{5} x + 5

f^{^{'}} (x) = g (x)

であれば

f (x) = \int g (x) d x

f (x) x^{- 1} f (x) = \int \frac{1}{5} x + 5 d x

\int \frac{1}{5} x + 5 d x = \frac{x ^{2}}{10} + 5 x + c_{1}

f (x) x^{- 1} f (x) = \frac{x ^{2}}{10} + 5 x + c_{1}

分離する

f (x) : f (x) = \frac{x ^{2} + 50 x + 10 c _{1}}{10} x, f (x) = - \frac{x ^{2} + 50 x + 10 c _{1}}{10} x

f (x) = \frac{x ^{2} + 50 x + 10 c _{1}}{10} x, f (x) = - \frac{x ^{2} + 50 x + 10 c _{1}}{10} x

簡素化

f (x) = \frac{x ^{2} + 50 x + c _{1}}{10} x, f (x) = - \frac{x ^{2} + 50 x + c _{1}}{10} x