derivative of (y-1^2)=4(x+2)

解

\frac{d}{d x} ((y - 1)^{2}) = 4 (x + 2)

y = 4 (\frac{x ^{2}}{2} + 2 x) + c_{1} + 1, y = - 4 (\frac{x ^{2}}{2} + 2 x) + c_{1} + 1

解答ステップ

\frac{d}{d x} ((y - 1)^{2}) = 4 (x + 2)

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

であれば

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

(y - 1)^{2} = \int 4 (x + 2) d x

\int 4 (x + 2) d x = 4 (\frac{x ^{2}}{2} + 2 x) + c_{1}

(y - 1)^{2} = 4 (\frac{x ^{2}}{2} + 2 x) + c_{1}

分離する

y : y = 4 (\frac{x ^{2}}{2} + 2 x) + c_{1} + 1, y = - 4 (\frac{x ^{2}}{2} + 2 x) + c_{1} + 1

y = 4 (\frac{x ^{2}}{2} + 2 x) + c_{1} + 1, y = - 4 (\frac{x ^{2}}{2} + 2 x) + c_{1} + 1