derivative of 7x^2+8ln(xy)=14

解

\frac{d}{d x} (7 x^{2} + 8 ln (x y)) = 14

y = \frac{e ^{\frac{14 x + c _{1} - 7 x ^{2}}{8}}}{x}

解答ステップ

\frac{d}{d x} (7 x^{2} + 8 ln (x y)) = 14

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

であれば

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

7 x^{2} + 8 ln (x y) = \int 14 d x

\int 14 d x = 14 x + c_{1}

7 x^{2} + 8 ln (x y) = 14 x + c_{1}

分離する

y : y = \frac{e ^{\frac{14 x + c _{1} - 7 x ^{2}}{8}}}{x}

y = \frac{e ^{\frac{14 x + c _{1} - 7 x ^{2}}{8}}}{x}